Answer:
a) The 90% confidence interval would be given by (230.212;233.128)
b) For this case if we analyze the confidence interval we see that not contains the value of 235. So we can't support the claim that the true mean is higher than 235 Hz at 10% of significance.
Step-by-step explanation:
Previous concepts and data given
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Data: 230.66, 233.05, 232.58, 229.48, 232.58
We can calculate the mean and the deviation from these data with the following formulas:
[tex]\bar X= \frac{\sum_{i=1}^n x_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=231.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=1.531 represent the sample standard deviation
n=5 represent the sample size
Part a) Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=5-1=4[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,4)".And we see that [tex]t_{\alpha/2}=2.13[/tex]
Now we have everything in order to replace into formula (1):
[tex]231.67-2.13\frac{1.531}{\sqrt{5}}=230.212[/tex]
[tex]231.67+2.13\frac{1.531}{\sqrt{5}}=233.128[/tex]
So on this case the 90% confidence interval would be given by (230.212;233.128)
Part b) Do the results of your calculations support the claim that mean natural frequency is 235 Hz?
For this case if we analyze the confidence interval we see that not contains the value of 235. So we can't support the claim that the true mean is higher than 235 Hz at 10% of significance.
To determine the 90% confidence interval for mean natural frequency, calculate the mean, standard deviation, find the t-value, and compute the margin of error and CI. The claim that the mean frequency is 235 Hz is assessed by checking if this value is within the calculated CI.
Explanation:To find the 90% two-sided confidence interval (CI) on mean natural frequency for the five delaminated beams, we first calculate the mean (\( \bar{x} \)) and the standard deviation (s) of the given frequencies. Then, we use the t-distribution, as the sample size is small (n=5), to find the t-value for a 90% CI, which corresponds to a significance level (alpha) of 0.10 and degrees of freedom (df) of n-1. Finally, we apply the formula for the 90% CI as follows:
Calculate the mean: \( \bar{x} = (230.66 + 233.05 + 232.58 + 229.48 + 232.58) / 5 = 231.67 \) Hz.Calculate the standard deviation (s):(b) To assess whether the mean natural frequency is 235 Hz, we would check if this value lies within the 90% CI. If it does not, the results do not support the claim that the mean natural frequency is 235 Hz.
If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places, .XXXX)
a) getting a sum of 1?
b) getting a sum of 5?
c) getting a sum of 12?
Answer: The required probabilities are
[tex](a)~0\\\\(b)\dfrac{1}{9},\\\\(c)~\dfrac{1}{36}.[/tex]
Step-by-step explanation: Given that a pair of fair dice is rolled.
We are to find the probability of getting
(a) getting a sum of 1.
b) getting a sum of 5.
c) getting a sum of 12.
Let S be the sample space for the experiment of rolling a pair of fair dice.
Then, S = {(1,1), (1,2), (1,3), (1, 4), (1,5), (1,6), . . . , (6,5), (6,6)}.
And, n(S) =36.
(a) Let E denote the event of getting a sum of 1.
Since the sum of the numbers on two dice is minimum 2, so
E = { } ⇒ n(E) = 0.
Therefore, the probability of event E is
[tex]P(E)=\dfrac{n(E)}{n(S)}=\dfrac{0}{36}=0.[/tex]
(b) Let F denote the event of getting a sum of 5.
Then,
F = {(1,4), (2,3), (3,2), (4,1)} ⇒ n(F) = 4.
Therefore, the probability of event F is
[tex]P(F)=\dfrac{n(F)}{n(S)}=\dfrac{4}{36}=\dfrac{1}{9}.[/tex]
(c) Let G denote the event of getting a sum of 12.
Then,
G = {(6,6)} ⇒ n(G) = 1.
Therefore, the probability of event G is
[tex]P(G)=\dfrac{n(G)}{n(S)}=\dfrac{1}{36}.[/tex]
Thus, the required probabilities are
[tex](a)~0\\\\(b)\dfrac{1}{9},\\\\(c)~\dfrac{1}{36}.[/tex]
The probability of getting a sum of 1, the sum of 5, and the sum of 12 are 0, 1/9, and 1/36 respectively
Probability is the likelihood or chance that an event will occur.
For a pair of rolled dice, the total outcome will be 6² = 36
Probability = Expected outcome/Total outcome
a) Pr(getting a sum of 1) = 0/36 = 0
Note that since we have a pair of dice, the least sum we can have is 2
b) The event for getting a sum of 5 are (1, 4), (4, 1), (3, 2), (2, 3)
n(E) = 4
Pr( getting a sum of 5) = 4/36 = 1/9
c) The event for getting a sum of 12 are (6, 6)
n(E) = 1
Pr( getting a sum of 12) = 1/36
Hence the probability of getting a sum of 1, the sum of 5, and the sum of 12 are 0, 1/9, and 1/36 respectively
Learn more here: https://brainly.com/question/13604758
A plane traveled from California and back. It took one hour on the way out than it did on the way back. The plane's average speed out wad 300 mph. The speed on the way back was 350mph. How many hours did the trip out take?
Answer:
6 hours
Step-by-step explanation:
You can set up a chart:
R T D
O 300 1+x ~ O=out B=back R=Rate/Speed T=time D=distance
B 350 x ~
The distance is the same. On the way out the speed was 300 mph, so you can see where that is on the chart. And the speed back was 350 mph. It took an extra hour on the way out than on the way back, so you can call the way back's time x and then say the way out's time was x+1.
It's important to know that R times T = D
Therefore we can say 300(x+1)=D and 350(x)=D
Since the distance is the same, 300(x+1)=350(x)
Solve:
300(x+1)=350x
300x+300=350x
50x=300
x=6
Therefore, the trip out took 6 hours.
I hope that helps! :)
Answer:the trip out took 7 hours
Step-by-step explanation:
Distance travelled = speed × time
Let t represent the time it took the plane to travel from California.
It took one hour on the way out than it did on the way back. This means that the time it took the plane to return would be t - 1
The plane's average speed out ward 300 mph. Distance travelled when going out would be
300 × t = 300 = 300t
The speed on the way back was 350mph. Distance travelled when returning would be
350(t - 1) = 350t - 350
Since the distance is the same, it means that
300t = 350t - 350
350t - 300t = 350
50t = 350
t = 350/50 = 7
Time taken to go out is 7 hours
Help!!!
Given the function f(x) = x/3 + 7. Find the input for which f(x) = 13
[tex]
\begin{cases}
f(x)=x/3+7\\
f(x)=13
\end{cases}
[/tex]
We find that
[tex]13=x/3+7\Longrightarrow x=\boxed{18}[/tex]
Hope this helps.
5) The Queen Mary is a large cruise ship that has 8, 123, 700 cubic feet of cargo space. Express this number in scientific notation.
Explain in words how you converted the number of cubic feet into scientific notation?
Let U represent the set of people in a certain community who were asked if they subscribe to an information source. Let D ={ x ∈ U | x subscribes to The Daily Informer } and N ={ x ∈ U | x subscribes to News Magazine } (Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.
a. N ∪ D
b. ( N c ∩ D ) ∪ ( N ∩ D c )
c. N c ∩ D
d. ( N ∩ D )c
e. ( N c ∪ D ) ∩ ( N ∪ D c )
Answer:
b. [tex]( N^c \cap D ) \cup ( N \cap D^c )[/tex]
Step-by-step explanation:
Here,
N = { x ∈ U | x subscribes to News Magazine },
D = { x ∈ U | x subscribes to The Daily Informer },
Such that N∩D ≠ ∅,
Now, the number of the set of people surveyed who subscribe only News Magazine
= Subscribe News Magazine and not Daily Informer
= [tex]N\cap D^c[/tex]
Similarly, the number of the set of people surveyed who subscribe only Daily informer
= Subscribe Daily informer and not subscribe News Magazine
= [tex]D\cap N^c[/tex]
Hence, the set of people surveyed who subscribe to exactly one of the two news sources given
= Subscribe News Magazine and not subscribe Daily Informer or subscribe Daily informer and not subscribe News Magazine
[tex]= (N\cap D^c)\cup (D\cap N^c)[/tex]
[tex]=( N^c \cap D ) \cup ( N \cap D^c )[/tex]
The set of people who subscribe to exactly one of the two news sources is represented by ( Nc ∩ D ) ∪ ( N ∩ Dc ). This includes people who subscribe to The Daily Informer but not News Magazine and those who subscribe to News Magazine but not The Daily Informer.
Explanation:The set that represents the set of people surveyed who subscribe to exactly one of the two news sources, The Daily Informer (D) or News Magazine (N), can be written as ( Nc ∩ D ) ∪ ( N ∩ Dc ). The notation Nc represents the set of all people who do not subscribe to News Magazine and Dc represents the set of all people who do not subscribe to The Daily Informer. Thus, Nc ∩ D represents those who subscribe to The Daily Informer but not News Magazine, while N ∩ Dc represents those who subscribe to News Magazine but not The Daily Informer. The union of these two sets, denoted by ∪, represents the complete set of people who subscribe to exactly one of the two news sources.
https://brainly.com/question/15513632
#SPJ3
the units digit of a two digit number is 10. If the digits are reversed, the new number is 9 less than the original number. find the original number
Answer: the units digit has to be a 1 digit number not 2
Step-by-step explanation:
Eight-year-old Terry's performance on an intelligence test is at a level characteristic of an average 5-year-old. In other words, Terry was average for his age group. Which of the following is most likely Terry’s IQ score?
6
4
5
8
Answer:
5
Step-by-step explanation:
Assuming the intelligence test had 10 questions, since Terry was average for his age group, his most likely IQ score is 5
Northern Light Health Partners offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work. Based o n this information what is the probability that an employee selected at random will need either corrective shoes or major dental work?
Answer: Our required probability is 20%.
Step-by-step explanation:
Since we have given that
Probability of the employees needed corrective shoes = 8%
Probability of the employees needed major dental work = 15%
Probability of employees needed both corrective shoes and major dental work = 3%
So, we need to find the probability that an employee will need either corrective shoes or major dental work.
So, it becomes,
[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\\P(S\cup D)=8+15-3\\\\P(S\cup D)=23-3\\\\P(S\cup D)=20\%[/tex]
Hence, our required probability is 20%.
A Chevrolet was purchased for $23, 750 and a 20% down payment was made. Find the amount financed.
They put 20% down so that means 80% was financed ( 100% - 20% = 80%).
Multiply the purchase price by 80%:
23750 x 0.80 = $19,000 was financed.