Answer:
3.22% probability that the sample average is greater than $228,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 227000, \sigma = 8500, n = 110, s = \frac{8500}{\sqrt{110}} = 810.44[/tex]
What is the probability that the sample average is greater than $228,500?
This is 1 subtracted by the pvalue of Z when X = 228500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{228500 - 227000}{810.44}[/tex]
[tex]Z = 1.85[/tex]
[tex]Z = 1.85[/tex] has a pvalue of 0.9678
1 - 0.9678 = 0.0322
3.22% probability that the sample average is greater than $228,500
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. At how many seconds will the lights first blink at the same time?
Answer:
20 seconds
Step-by-step explanation:
The least common multiple of 4 and 5 is 20. So the two lights will blink at the same time every 20 seconds.
Based on the number of seconds it takes for each light to blink, they will both blink at 20 seconds.
The green light blinks every 4 seconds and the yellow, every 5 seconds.
The time that they will blink together depends on the lowest common multiple of both numbers.
Multiples of 4 = 4, 8, 12, 16, 20
Multiples of 5 = 5, 10, 15, 20
The lowest common multiple is 20 which means they will blink together after 20 seconds.
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The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1) is the square footage, the second independent variable (x2) is the number of bedrooms, and the third independent variable (x3) is the age of the house.
Effects on Selling Price of Houses
Square Feet Number of Bedrooms Age Selling Price
2049 5 5 282900
10101 4 8 268600
1033 3 9 137900
1286 2 8 114900
2920 4 4 113000
2443 10 10 154700
2206 2 5 234000
1360 3 4 183400
2405 3 1 193100
Copy Data
Step 1 of 2 :
Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
HOW TO PULL THIS UP IN EXCEL-----------------------------------------
To find the p-value from the given data in Excel, populate your data in Excel sheet into various columns for each variable. Then, use the 'Regression' tool under 'Data Analysis' in the 'Data' tab, selecting the appropriate ranges for dependent and independent variables. Ensure that the 'P-Values' box is checked before clicking 'OK'. Excel will then generate the regression analysis with the p-value.
Explanation:In Excel, you can perform regression analysis to deduce the p-value from this data using the following steps:
First, you want to load your data into the Excel sheet. Each independent variable (Square Feet, Number of Bedrooms, Age) should have its own column and the dependent variable (Selling Price) too.Once the data is spread across columns, go to the 'Data' tab, under which you'll find 'Data Analysis'. If it's not visible, you'll have to add it in from 'Excel Options' > 'Add-Ins' > 'Excel Add-Ins' > 'Analysis ToolPak'.After clicking 'Data Analysis', a window will pop up. Choose 'Regression' and click 'OK'.A dialog box will appear. Under 'Input', select the Y Range (dependent variable: Selling Price) and X Range (independent variables: Square Feet, Number of Bedrooms, Age).Mark the box 'Labels' if you have header rows. Also check the box for 'P-Values'.Finally, click 'OK' and Excel will generate the regression analysis including the p-value for your data.Learn more about Regression Analysis and P-Value in Excel here:https://brainly.com/question/30590416
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How do you calculate the average mark?
Answer:
68.44%
Step-by-step explanation:
You compute the average the way you compute any average: add up the numbers and divide by their number.
Multiplication is a useful way to shorten the effort of repeated addition.
(64% × 3 + 58% × 7 + 88% × 3 +33% + 100% × 2)/(3 +7 +3 + 1 + 2)
= 1095%/16 = 68.4375%
≈ 68.44% . . . the average mark for the class
Four pencils are held together with a band.
Each of the pencils diameter 10mm.
Find the length of the band in this position
Give your answer in terms of π.
To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.
Explanation:To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.
What is the value of 7 in the number 8.07
0.07 or 7 hundredths.
need help with this question
Answer:
2√11
Step-by-step explanation:
The square of the hypotenuse (h) of the smaller triangle is given by the Pythagorean theorem:
h² = 6² +8² = 100
The length of x is given by that same theorem:
h² +x² = 12²
x² = 12² -h² = 144 -100 = 44 . . . . . subtract h², fill in its value
x = √44 . . . . . . . . take the square root
x = 2√11 . . . . . . . simplify the root
Navibulgar is a bulgarian shipping company. the department that handles fragile shipping rolls prints and other documents into cylinders and then pack the cylinders into special containers that are triangular solids so that the cylinders would not roll around in the trailers. the surface area of a triangular prism container that would be needed to enclose a rolled document with a diameter of 10cm and a length of 85 cm? Round your answer to the nearest square centimeter. Assume the triangle face is an equilateral triangle
Answer:
Was the answer possibly C) 4,671 sq.cm. ?
Explanation:
Since the expert didn't get it right from what I'm seeing.
The surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.
To calculate the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm, we follow these steps:
1. Determine the dimensions of the equilateral triangle base:
- The diameter of the cylinder (10 cm) is equal to the side length of the equilateral triangle base.
2. Calculate the height of the equilateral triangle:
- The height \( h \) of an equilateral triangle with side length \( a \) is given by:
[tex]\[ h = \frac{\sqrt{3}}{2} a \] For \( a = 10 \) cm: \[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66 \text{ cm} \][/tex]
3. Calculate the area of the equilateral triangle base:
- The area \( A \) of an equilateral triangle with side length \( a \) is given by:
[tex]\[ A = \frac{\sqrt{3}}{4} a^2 \] - For \( a = 10 \) cm: \[ A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.30 \text{ cm}^2 \][/tex]
4. Calculate the lateral surface area of the prism:
- The lateral surface area is given by the perimeter of the triangular base times the length of the prism.
- The perimeter \( P \) of an equilateral triangle with side length \( a \) is:
[tex]\[ P = 3a \] For \( a = 10 \) cm: \[ P = 3 \times 10 = 30 \text{ cm} \][/tex]
- The length of the prism is 85 cm.
- The lateral surface area \( L \) is:
[tex]\[ L = P \times \text{length} = 30 \times 85 = 2550 \text{ cm}^2 \][/tex]
5. Calculate the total surface area of the prism:
- The total surface area \( S \) includes the lateral surface area and the area of the two triangular bases.
- Total surface area \( S \) is given by:
[tex]\[ S = L + 2 \times A \] - Substitute the values: \[ S = 2550 + 2 \times 43.30 = 2550 + 86.60 = 2636.60 \text{ cm}^2 \][/tex]
6. Round the total surface area to the nearest square centimeter:
[tex]\( S \approx 2637 \text{ cm}^2 \)[/tex]
So, the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.
Christina saves her coins in a cube-shaped coin bank. Her coin bank is 7 inches wide and 7 inches tall. What is the volume of Christina's coin bank?
The volume of Christina's cube-shaped coin bank is calculated by cubing the length of one of its sides, which is 7 inches. The volume is therefore 7 × 7 × 7, or 343 cubic inches.
Explanation:The volume of Christina's cube-shaped coin bank can be calculated using the formula for the volume of a cube, which is Volume = side × side × side. As all sides of a cube are equal and the coin bank is 7 inches wide and 7 inches tall, we can calculate the volume by multiplying 7 inches by 7 inches by 7 inches.
Calculation:
Volume = 7 in. × 7 in. × 7 in. = 343 cubic inches
Hence, the volume of Christina's coin bank is 343 cubic inches.
Final answer:
The volume of Christina's cube-shaped coin bank is calculated using the cube volume formula and is found to be 343 cubic inches.
Explanation:
To calculate the volume of Christina's coin bank, we use the formula for the volume of a cube, which is Volume = side³, where 'side' is the length of one side of the cube. Since the coin bank is 7 inches wide and 7 inches tall, each side is 7 inches. Thus, the volume of the coin bank is:
Volume = 7 in. × 7 in. × 7 in. = 343 in.³
Therefore, Christina's coin bank has a volume of 343 cubic inches.
An office manager just got back from vacation, so she has a pile of 424 letters to read. Then, the mail carrier comes and delivers 41 more letters for her. How many letters does the office manager have now?
465
383
455
373
Answer:
465
Step-by-step explanation:
424+41=465
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.
Answer:
A, B, D
Step-by-step explanation:
The linear parent function is a straight line with equation x=y, which means that it has a slope of 1 and goes through the origin. However, it does not go through quadrants 2 and 4, only 1 and 3. Hope this helps!
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 5.2 and 1.8 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.2. Find the mean and standard deviation of the corrected pH measurements.
Answer:
mean = 7.98; standard deviation = 2.52
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 7 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 57 customers taken after these changes were made produced a mean waiting time of 6.5 minutes with a standard deviation of 2.1 minutes. Using this sample mean, the bank manager displayed a huge banner inside the bank mentioning that the mean waiting time for customers has been reduced by new changes. Do you think the bank manager’s claim is justifiable? Use a 10% significance level to answer this question. Use both approaches.
Answer:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=6.5[/tex] represent the sample mean for tje waiting times
[tex]s=2.1[/tex] represent the sample standard deviation
[tex]n=57[/tex] sample size
[tex]\mu_o =7[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean for this case is less than 7 minutes, the system of hypothesis for this case sre:
Null hypothesis:[tex]\mu \geq 7[/tex]
Alternative hypothesis:[tex]\mu < 7[/tex]
Since we don;t know the population deviation the statistic for the t test is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
If we replace the info given we got:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Following are the solution to the given question:
Given:
size [tex](n) = 58[/tex]
mean [tex]\mu = 7.4 \ minutes[/tex]
standard deviation [tex]\sigma = 2.3 \ minutes[/tex]
null and alternative hypotheses:
[tex]H_0 : \mu = 8 \ minutes\\\\H_a : \mu < 8 \ minutes\\\\[/tex]
Calculating the test statistic:
So, the observed value
Calculating the degrees of freedom:
[tex]\to 58 - 1 = 57[/tex]
Calculating the range of p-value:
Therefore the t is the critical value at the significance level that is 0.05 with of freedom is,
Therefore,
[tex]\to test \ statistic = -1.987 < -1.672[/tex] rejecting the null hypothesis.
Therefore, the conclusion of the manager's claim is "True".
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2x+9+3x+x=
what is it in all 3 solutions
Answer:
6x+9
3(2x+3)
Step-by-step explanation:
Combine like terms
2x+9+3x+x
6x+9
We can factor out 3
3(2x+3)
Answer:
6x + 9
Step-by-step explanation:
2x + 9 + 3x + x =
6x + 9
A spinner has a 12 equal sized sections. Three of the sections are orange. What is the probability that the spinner will land on orange?
1/4
Step-by-step explanation:
1/4 is the original fraction of 3/12 simplified
Final answer:
The probability of the spinner landing on an orange section is 1/4 or 0.25, meaning there is a 25% chance it will land on orange.
Explanation:
The question involves calculating the probability of a spinner landing on a specific color. If a spinner has 12 equal-sized sections and three of them are orange, to find the probability of landing on orange, we use the ratio of the number of orange sections to the total number of sections. In this case, there are 3 orange sections and 12 sections in total, so the probability (P) is:
P(orange) = Number of orange sections / Total number of sections
P(orange) = 3 / 12
P(orange) = 1 / 4
Therefore, the probability that the spinner will land on orange is 1/4 or 0.25, which means there's a 25% chance the spinner will land on an orange section.
Each group of students receives a bag that has 8 red cubes, 2 green cubes, and 10 blue cubes. If each group makes 100 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?
Answer:
10 green cubes
Step-by-step explanation:
The total number of cubes is 8+2+10 = 20
The probability of drawing a green cube when there is replacement is
P(green) = green cubes/ total
=2/ 20
= 1/10
Multiply the probability by the number of draws to get the total number of cubes
1/10 * 100 draws = 10 green cubes
Expect 10 green cube draws in 100 pulls, with 8 red and 10 blue cubes also present.
To calculate the expected number of times a green cube is drawn, we can use the concept of probability.
In each pull, there are 20 cubes in total (8 red + 2 green + 10 blue). So, the probability of drawing a green cube in a single pull is:
[tex]\[ P(\text{green}) = \frac{\text{number of green cubes}}{\text{total number of cubes}} = \frac{2}{20} = \frac{1}{10} \][/tex]
Since each pull is independent and the cubes are replaced after each pull, the probability of drawing a green cube remains the same for each pull.
Therefore, the expected number of times a green cube is drawn in 100 pulls is:
[tex]\[ \text{Expected number of green draws} = P(\text{green}) \times \text{Total number of pulls} = \frac{1}{10} \times 100 = 10 \][/tex]
So, you would expect them to draw a green cube about 10 times in 100 pulls.
A local hotel wants to estimate the average age of its guests that are from out-of-state. Preliminary estimates are that standard deviation of population of guests from out-of-state is 30. How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence? a. 12 b. 11 c. 139 d. 138
Answer:
c. 139
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?
We need a sample size of n.
n is found when [tex]M = 5, \sigma = 30[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 1.96*30[/tex]
Simplifying by 5
[tex]\sqrt{n} = 1.96*6[/tex]
[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]
[tex]n = 138.30[/tex]
We round up,
So the correct answer is:
c. 139
Answer:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
Step-by-step explanation:
For this case we have this previous info:
[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation
[tex]Confidence =0.95[/tex] represent the confidence level
The margin of error for the true mean is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
Am isosceles triangle has at least 2 equal sides and equilateral triangle has all sides equal which sentence is true
all isosceles triangles are equilateral triangle
all equilateral triangles are isosceles triangles all equilateral triangles does not necessarily have to be isosceles triangles
An isosceles triangle cannot be an equilateral triangle
Answer:an isosceles triangle cannot be an equilateral triangle
Step-by-step explanation:
An isosceles triangle cannot be an equilateral triangle
Final answer:
An isosceles triangle has at least 2 equal sides and an equilateral triangle has all sides equal. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.
Explanation:
An isosceles triangle has at least 2 equal sides, while an equilateral triangle has all sides equal. Therefore, the sentence 'All isosceles triangles are equilateral triangles' is not true because not all isosceles triangles have all sides equal. On the other hand, the sentence 'All equilateral triangles are isosceles triangles' is true because every equilateral triangle automatically has at least 2 equal sides. Furthermore, it is possible for an equilateral triangle to not be an isosceles triangle if all three sides are not equal in length. So, the sentence 'An isosceles triangle cannot be an equilateral triangle' is not true.
Which measure of central tendency is MOST EASILY affected by outliers? A) mean Eliminate B) median C) mode D) IQR
Answer: A. Mean.
Explanation:
Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.
The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.
Answer:
A) mean
Step-by-step explanation:
Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
Answer:
[tex]\sqrt[4]{10x^2}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{5x}.\sqrt[4]{2x} = \sqrt[4]{5x * 2x} = \sqrt[4]{10x^2}[/tex]
Answer:
(10x²)^¼
Or,
10^¼ × x^½
Step-by-step explanation:
(5x)^¼ × (2x)^¼
[5x × 2x]^¼
(10x²)^¼
10^¼ × (x²)^¼
10^¼ × x^½
Consider two populations for which μ1 = 35, σ1 = 3, μ2 = 20, and σ2 = 4. Suppose that two independent random samples of sizes n1 = 47 and n2 = 54 are selected. Describe the approximate sampling distribution of x1 − x2 (center, spread, and shape). What is the shape of the distribution? The distribution would be non-normal. The distribution is approximately normal. The shape cannot be determined. What is the mean of the distribution? What is the standard deviation of the distribution?
Answer:
The distribution is approximately normal.
The mean and standard deviation are 15 and 0.98 respectively.
Step-by-step explanation:
The population of the random variables X₁ and X₂ are distributed as follows:
[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]
Two independent random samples of sizes,
[tex]n_{1}=47\\\\n_{2}=54[/tex]
are selected form the two populations.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]
So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.
Then, the distribution of [tex]\bar X_{1}[/tex] is:
[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]
And the distribution of [tex]\bar X_{2}[/tex] is:
[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]
If two random variables are normally distributed then their linear function is also normally distributed.
So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.
The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]
The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]
*X₁ and X₂ are independent.
Thus, the mean and standard deviation are 15 and 0.98 respectively.
Find the 12th term of the geometric sequence 1,−2,4
Answer:-2048
Step-by-step explanation:
First term(a)=1
Common ratio(r)=-2/1 or 4/-2
Common ratio(r)=-2
nth term=a x r^(n-1)
12th term=1 x (-2)^(12-1)
12th term=1 x (-2)^11
12th term=(-2)^11
12th term=-2048
The 12th term of the geometric sequence 1, −2, 4, .... is equal to -2048.
How to calculate the nth term of a geometric sequence?In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where:
[tex]a_n[/tex] is the nth term of any geometric sequence.r represents the common ratio.[tex]a_1[/tex] represents the first term of any geometric sequence.In this context, the common ratio would be determined as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -2/1
Common ratio, r = -2
Now, we can determine the 12th term in the sequence defined by this explicit rule;
[tex]a_n=a_1(r)^{n-1}\\\\a_{12}=1(-2)^{12-1}\\\\a_{12}=(-2)^{-11}\\\\a_{12}=-2048[/tex]
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The two box plots show the data of the pitches thrown by two pitchers throughout the season. Which statement is correct? Check all that apply.
Answer:
Doesn’t show image
Step-by-step explanation:
Answer:
B,C
Step-by-step explanation
Pitcher 1 does not have a symmetric data set.
Pitcher 2 has a symmetric data set.
A store stocked 150 bundles of Charmin Extra Soft and Fluffy toilet tissue for a weekend sale. Last weekend, 72 bundles of the Charmin Extra Soft and Fluffy toilet tissue were sold. What percent of the
bundles of stocked Charmin Extra Soft and Fluffy toilet paper were sold that weekend?
Answer:
48% was sold
Step-by-step explanation:
Let the percent sold be x
x/100 * 150 = 72
(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)
Simplifying...
150x/100 = 72
3x/2 = 72
3x = 144
x = 48%
Write an expression, using an exponent, that is equivalent to 9 x 9 x 9 x 9 x 9 x 9 x 9.
Answer:
[tex]9^{2}[/tex]
Step-by-step explanation:
Answer:
[tex]9^{7}[/tex]
Step-by-step explanation:
There are 7 9s being multiplied together. This can be written as 9 to the 7th power or [tex]9^{7}[/tex]
James and Karlee caught a lizard in their backyard. Its length from head to the end of the tail is
3/5 meters and the length of its tail is1/5
Answer:
what do you need answered?
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
khan academy
Find the slope of the line passing through the points (-9. -6) and (-4, 5)
Answer:
The slope of the line is 2.2 or 11/5
Step-by-step explanation:
I graphed the points on the graph below and found the slope of the line.
The slope of the line is 11/ 5.
What is the slope of a line?The slope is equal to the change in y over the change in x, or rise over run.
m = change in y/change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m = (y₂−y₁)/(x₂−x₁)
Substituting the values of x and y into the equation to find the slope.
m = (5 − ( − 6 ))/(−4−(−9))
m =11/5
Therefore, the Slope of the line is 11/ 5.
To learn more about the slope of the line refer to :
https://brainly.com/question/16949303
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A 3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $
Answer:
$3,256.2
Step-by-step explanation:
First, we need to get 3% of 3,460. Find the decimal value of 3%:
3% -> [tex]\frac{3}{100}[/tex] -> 0.03
Next, lets multiply 3,460 by 0.03:
[tex]x=3,460(0.03)[/tex]
[tex]x=103.8[/tex]
Now subtract that number from 3,460:
[tex]3,460-103.8=3,356.2[/tex]
Lastly, lets take the $100 fee off of the number we just got:
[tex]3,356.2-100=3,256.2[/tex]
The new amount is $3,256.2
Answer:
3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $3,256.2.
explanation:
The use of social networks has grown dramatically all over the world. In a recent sample of 24 American social network users and each was asked for the amount of time spent (in hours) social networking each day. The mean time spent was 3.19 hours with a standard deviation of 0.2903 hours. Find a 99% confidence interval for the true mean amount of time Americans spend social networking each day
Answer:
The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
Step-by-step explanation:
The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]
Confidence level = 99%.
Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]
*Use a t-table.
Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]
Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
A research center poll showed that 81% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Answer:0.19
Step-by-step explanation:
n a survey of 700 year 2005 high school graduates, it was found that 50.3% had enrolled in colleges, 11.1% in vocational institutions, while the other 38.6% did not pursue any further studies. Perform a test of hypotheses to determine whether the college enrollment rate in the population of year 2005 high school graduates was significantly higher than 48%. (Calculate the P-value.) Round to four decimal places.
Answer:
[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]
Now we can calculate the p value given by:
[tex]p_v =P(z>1.218)=0.1116[/tex]
Step-by-step explanation:
Information provided
n=700 represent the random sample selected
[tex]\hat p=0.503[/tex] estimated proportion of college enrollment
[tex]p_o=0.48[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value (variable of interest)
System of hypothesis
we want to check if the true proportion for the college enrollment is higher thna 0.48, the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.48[/tex]
Alternative hypothesis:[tex]p > 0.48[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we have:
[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]
Now we can calculate the p value given by:
[tex]p_v =P(z>1.218)=0.1116[/tex]