The following table shows the probability distribution for a discrete random variable.
X 13| 16 |17| 21| 23| 25 |26 |31
P(X) 0.07 |0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08
What is the mean of this discrete random variable. That is, what is E(X), the expected value of X?

Answers

Answer 1

X    | 13 |    16 | 17|    21|    23|    25 | 26 | 31| |
------------|-----------------------------------------------------------------|.
P(X) | 0.07 | 0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08 |
------------|-----------------------------------------------------------------|
X.P(X)    | 0.91 | 3.36| 2.89| 5.25| 1.15| 1.00| 3.38| 2.48 |
------------|-----------------------------------------------------------------|

E(X) = ∑(X.P(X) =(0.91+3.36+2.89+ 5.25+ 1.15+ 1.00+ 3.38+ 2.48)

E(X) = ∑(X.P(X) = 20.42

Pls review the calculation to be on the safe side

Answer 2

Answer: APEX- 20.42

Step-by-step explanation: Multiply 13 by 0.07, multiply 16 by 0.21, and so on. then add up all of the decimals and that is your answer

Related Questions

Evaluate the surface integral. (give your answer correct to at least three decimal places.) s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2

Answers

Split up the surface [tex]S[/tex] into three main components [tex]S_1,S_2,S_3[/tex], where

[tex]S_1[/tex] is the region in the plane [tex]y=0[/tex] bounded by [tex]x^2+z^2=1[/tex];

[tex]S_2[/tex] is the piece of the cylinder bounded between the two planes [tex]y=0[/tex] and [tex]x+y=2[/tex];

and [tex]S_3[/tex] is the part of the plane [tex]x+y=2[/tex] bounded by the cylinder [tex]x^2+z^2=1[/tex].

These surfaces can be parameterized respectively by

[tex]S_1:~\mathbf s_1(u,v)=\langle u\cos v,0,u\sin v\rangle[/tex]
where [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex],

[tex]S_2:~\mathbf s_2(u,v)=\langle\cos v,u,\sin v\rangle[/tex]
where [tex]0\le u\le2-\cos v[/tex] and [tex]0\le v\le2\pi[/tex],

[tex]S_3:~\mathbf s_3(u,v)=\langle u\cos v,2-u\cos v,u\sin v\rangle[/tex]
where [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex].

The surface integral of a function [tex]f(x,y,z)[/tex] along a surface [tex]R[/tex] parameterized by [tex]\mathbf r(u,v)[/tex] is given to be

[tex]\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\iint_Sf(\mathbf r(u,v))\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times\frac{\partial\mathbf r(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv[/tex]

Assuming we're just finding the area of the total surface [tex]S[/tex], we take [tex]f(x,y,z)=1[/tex], and split up the total surface integral into integrals along each component surface. We have

[tex]\displaystyle\iint_{S_1}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}u\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle\iint_{S_1}\mathrm dS=\pi[/tex]

[tex]\displaystyle\iint_{S_2}\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2-u\cos v}\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle\iint_{S_2}\mathrm dS=4\pi[/tex]

[tex]\displaystyle\iint_{S_3}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\sqrt2u\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle\iint_{S_3}\mathrm dS=\sqrt2\pi[/tex]

Therefore

[tex]\displaystyle\iint_S\mathrm dS=\left\{\iint_{S_1}+\iint_{S_2}+\iint_{S_3}\right\}\mathrm dS=(5+\sqrt2)\pi\approx20.151[/tex]

The process of using sample statistics to draw conclusions about population parameters is called

Answers

The process of using sample statistics to draw conclusions about population parameters is called Statistical Inference.
Statistical Inference are based on samples.Sometimes there are errors in this samples.Statistical inference can be contrasted with descriptive statistics.
It is also the process of using sample statistics to draw scientific truths from data.

A local hamburger shop sold a combined total of 436 hamburger and cheeseburgers on Friday. There were 64 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?

Answers

64 fewer cheeseburgers were sold than hamburgers. The total number of hamburgers sold on Friday was 250.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

Total number of hamburgers and cheeseburgers sold on Friday: 436.

The number of cheeseburgers sold was 64 fewer than the number of hamburgers.

The objective is to find the number of hamburgers sold on Friday.

To find out how many hamburgers were sold on Friday,

Set up a system of equations.

Let's denote the number of hamburgers as 'H' and the number of cheeseburgers as 'C'.

From the given information,

The total number of hamburgers and cheeseburgers sold is 436,

So write the equation,

H + C = 436.

Since there were 64 fewer cheeseburgers sold than hamburgers,

Which can be written as C = H - 64.

Now substitute the second equation into the first equation and solve for H:

H + (H - 64) = 436

Combine like terms,

2H - 64 = 436

Add 64 to both sides,

2H = 500.

Divide both sides by 2,

H = 250.

Hence,

250 hamburgers were sold on Friday.

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** NEED THIS ANSWERED ASAP**

Find the indicated probability. Round to the nearest thousandth.

In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive?

a. 0.503
b. 0.00000177
c. 1.00
d. 0.497

Answers

A: you can find this by finding the complement, that being if all of the blood samples were negative, and then subtracting that from one. The probability of one blood sample testing negative is 0.89, raising that to the 6th power due to the 6 blood samples gives us about 0.497, and subtracting that from one gives us a, 0.503.

Write the fractions in order from smallest to largest. 7/10, 3/20,22/25, 2/25

Answers

7/10 = 0.7
3/20 = 0.15
22/25 = 0.88
2/5 = 0.4

order from smallest to largest
3/20, 2/5, 7/10 and 22/25

I believe the order from smallest to largest would be:
2/25, 3/20, 7/10, 22/25

Suppose a and b give the population of two states where a>b . Compare the expressions and tell which of the given pair is greater or if the expression are equal.

b/a+b and 0.5

Answers

Suppose a = b, then [tex]\frac{b}{a+b}=\frac{b}{b+b}=0.5[/tex]

Since a > b, then a + b > b + b and thus [tex]\frac{b}{a+b}<\frac{b}{b+b}[/tex]

Therefore, [tex]\frac{b}{a+b}<0.5[/tex]

The nutritional chart on the side of a box of a cereal states that there are 93 calories in a three fourths 3/4 cup serving. How many calories are in 5 cups of the cereal?

Answers

The answer for this question will be 620 calories.
In this case, 3/4 cup= 93 calories and you need 5 cups. First you need to count calorie per cups, it would be 1 cup/(3/4 cup) * 93 calorie = 124 calorie/cup.
Then 5 cup of cereal would be 5*124 calorie= 620 calories.

A store stocked 150 cans of popcorn for a weekend sale.
That weekend, 72 of the cans sold. What percent of the
cans of popcorn stocked were sold that weekend?

Answers

Answer:

48%

Step-by-step explanation:

In order to find the percentage we need to divide the sold cans by total cans and multiply the result by 100.

Total cans = 150

Sold cans = 72

→ 72/150 = 0.48

→ 0.48 * 100 = 48

The percentage of the cans of popcorn stocked were sold that weekend is 48%

The given parameters are:

Total can of popcorn = 150

Sold can of popcorn = 72

The percentage of can sold is then calculated as:

[tex]\%Sold = \frac{72}{150} *100\%[/tex]

Multiply 72 and 100

[tex]\%Sold = \frac{7200}{150}\%[/tex]

Divide 7200 by 150

[tex]\%Sold = \%48[/tex]

Hence, the percentage of the cans of popcorn stocked were sold that weekend is 48%

Answers

so... let's say the amounts invested were "a" at 6% and "b" at 7.5%.

ok.. hmm what's 6% of a? well, (6/100) * a or 0.06a.
what's 7.5% of b? well, (7.5/100) * b or 0.075b.

now... we know, whatever "a" and "b" are, they total the investment of 5000 bucks, thus a + b = 5000

and the interest yielded was 337.50, thus 0.06a + 0.075b = 337.50

thus [tex]\bf \begin{cases} a+b=5000\implies \boxed{b}=5000-a\\ 0.06a+0.075b=337.50\\ ----------\\ 0.06a+0.075\left( \boxed{5000-a} \right)=337.50 \end{cases}[/tex]

solve for "a", to see how much was invested at 6%.

what about "b"? well, b = 5000 - a.

X = amount invested in bonds (5000-X) = amount invested in money mkt
X (.06) + (5000-X)(.075) = 337.50
.06X + 375 - .075 X = 337.50
375 - 337.50 = .075 X - .06X
37.50 = .015 X
X = $2500 invested in bonds

Blue shaded 20 squares on his hundreds grid. Becca shaded 30 squares on her hundreds grid. Write two decimals greater than Luke decimal in less than Bekkas decimal

Answers

Attached is the answer to your question.

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (1 point)

Answers

The equation of the parabola with the given dimensions and vertex at the origin is y = -4x^2.

Finding the Equation of a Parabola

To find the equation of a parabola with a vertex at the origin and given dimensions, we can use the standard form of a parabolic equation, which is y = ax^2. In this case, since the parabola opens downward and the vertex is at the origin (0,0), the equation will have the form y = -ax^2. The value of 'a' can be determined using the dimensions provided for the parabola, which are a width of 42 feet (meaning that the points (21,0) and (-21,0) are on the parabola) and a height of 84 feet (the y-coordinate at the vertex).

Since the point (21, 0) lies on the parabola, substituting it into the equation y=-ax^2 gives us 0 = -a(21)^2, which leads us to find that a = -84/(21)^2. Substituting the value of 'a' back into the equation gives us the final equation of the parabola: y = -84/(21)^2
x^2.

The equation of the parabola is: [tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex] .

To find the equation of the parabola with its vertex at the origin, we can use the standard form of a parabolic equation, which is [tex]$ y = ax^2 $.[/tex]

Given that the parabola opens downwards, we know that a must be negative. To determine the value of ( a ), we need to find a point on the parabola.

We're given the dimensions of the arch: 84 feet high and 42 feet wide at the base. Since the arch is symmetrical, the highest point is at the midpoint of the base, which is ( x = 0 ). At this point,( y = 84 ).

So, substituting the coordinates of this point into the equation, we get:

[tex]\[ 84 = a \times 0^2 \][/tex]

This simplifies to ( 84 = 0 ), which doesn't give us any useful information. Instead, we need to consider another point on the parabola.

Since the arch is symmetric, we can choose a point where ( x = 21 ) (half of the width of the base), and ( y = 0 ).

Substituting these coordinates into the equation, we get:

[tex]\[ 0 = a \times (21)^2 \][/tex]

0 = 441a

Dividing both sides by 441, we find ( a = 0 ). However, this seems incorrect, as it would mean the arch is just a straight line, which it isn't. This suggests that our choice of coordinates may not be correct.

Let's reconsider. The midpoint of the base is x = 0, but the highest point might not be there. Instead, let's choose a point where ( x = 0 ) and ( y = 42 ), as this is the highest point of the arch.

Substituting these coordinates into the equation, we get:

[tex]\[ 42 = a \times 0^2 \][/tex]

42 = 0

This also doesn't give us useful information. It seems we might have approached this problem incorrectly. Let's try a different strategy.

Since we know the arch is a parabolic shape, and the parabola opens downwards, we can write its equation in the form:

[tex]\[ y = ax^2 + c \][/tex]

To find the values of a and c , we need two points on the parabola. We already have one: the highest point of the arch, which is at x = 0 and (y = 42 ).

Now, we need to find another point. Since the arch is symmetric, we can use any point along the base. Let's choose the point where x = 21 , which is half of the width of the base. At this point, y = 0 .

Substituting these points into the equation, we get:

[tex]\[ 42 = a \times 0^2 + c \][/tex]

[tex]\[ 0 = a \times 21^2 + c \][/tex]

The first equation simplifies to ( c = 42 ).

Substituting this value of ( c ) into the second equation, we get:

[tex]\[ 0 = a \times 21^2 + 42 \][/tex]

Solving for a :

[tex]\[ a \times 441 = -42 \][/tex]

[tex]\[ a = \frac{-42}{441} \][/tex]

[tex]\[ a = -\frac{2}{21} \][/tex]

So, the equation of the parabola is:

[tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex]

Given a mean of 8 and a standard deviation of 0.7, what is the z-score of the value 9 rounded to the nearest tenth?

Answers

[tex]\mu[\tex]=8
[tex]\sigma[\tex]=0.7
x=9

Z=(x-[tex]\mu[\tex])/[tex]\sigma[\tex]
=(9-8)/0.7
=1.43
=1.4 [to the nearest tenth]

Answer: The z-score of the value 9 rounded to the nearest tenth = 1.4

Step-by-step explanation:

Given: Mean [tex]\mu=8[/tex]

Standard deviation [tex]\sigma=0.7[/tex]

The given random value x= 9

Now, the formula to calculate the z score is given by:-

[tex]z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ z=\dfrac{9-8}{0.7}\\\\\Rightarrow\ z=1.42857142857\approx1.4[/tex]

Hence, the z-score of the value 9 rounded to the nearest tenth = 1.4

a patio is in the shape of a regular octagon. the sides have length 5m. Calculate the area of the patio

Answers

here is the solution.

Round the answer as needed.

If I had a board that was 11 1/2 feet long and wanted to give it to 7 boys in equal pieces how long would each piece be?

Answers

11.5 divided by 7.5 = 1.6429, don't know what you are rounding the answer to, but each boy receives about 1.64 feet of the board.

Simple interest formula: P=Irt
Solve for t

Answers

the formula should be I=Prt but whatever

if you had I=Prt then divide both sides by Pr to get I/(Pr)=t

if you want to use P=Irt, divide both sides by Ir to get P/(Ir)=t

The value of t in the simple interest formula P = Irt is t = P / (Ir).

To solve the simple interest formula P = Irt for t, we need to isolate the variable t on one side of the equation.

The formula can be rearranged as follows:

P = Irt

First, divide both sides of the equation by I:

P/I = rt

Next, divide both sides of the equation by r:

(P/I) / r = t

Simplifying further:

t = P / (Ir)

Therefore, the value of t in the simple interest formula P = Irt is t = P / (Ir).

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twice a number and 5 more is 100

Answers

Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering this question today, and will be teaching you how to handle it on your own in the future.

First, let's take a look at our problem.
"Twice a number and 5 more is 100."
Based on this context, we are looking for a specific number to plug in.

To solve for this, I will rewrite the problem. As I do so, I will be writing (in parenthesis) the translation of an equation.

Twice a number (2x) and 5 more (+5) is 100 (=100).

Let's rewrite everything that's in parenthesis.
2x + 5 = 100

This is our equation.
To solve for this, we will need to do some basic algebra. Of course, I will teach you how to handle this on your own in future scenarios.

2x + 5 = 100
To solve for x, we need to isolate 2x, and then divide both sides by 2.

2x + 5 = 100
Subtract 5 from both sides to isolate 2x.
5 - 5 = 0
100 - 5 = 95

We now have the following equation:
2x = 95
Divide both sides by 2 to solve for x.

2x / 2 = x
95 / 2 = 47.5

x = 47.5

47.5 is your number.

I hope this helps!

You've decided you want a plant for your room. At the gardening store, there are 4 different kinds of plants (tulip, fern, cactus, and ficus) and 4 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?

Answers

First find how many possibilities there are total. We can find this simply by multiplying the total number of plants, by the total number of pots.

4 x 4 = 16

There are 16 possibilities in all.
The probability that you'll end up with a tulip in a plastic pot is 1/16, because there's only one way to get a tulip in a plastic pot out of all 16.

The answer is 1/16. :)

The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Answers

The coefficients of a binomial expansion are determined by the Pascal's triangle.

Take a look at the picture.

draw the Pascal's triangle up to the third row. (the row with only 1 is the zero'th row)

Also, notice that as we expand [tex](A+B) ^{3} [/tex],
in each term the power of A decreases by 1, starting from 3, and the powers of B increase by 1, up to 3.

According to these, the second term of [tex](A+B) ^{3} [/tex] is
[tex]3A^{2}B [/tex],

where A=4x, and B=3y,

substituting A an B:

[tex]3A^{2}B=3(4x)^{2}(3y)=3*16 x^{2} *3y=144 x^{2} y[/tex]

Answer: 144

How do you write an equation that shows an estimate of each answer for 503+69

Answers

You have to round to the nearest whole number so it would be 500 and 70
so the equation would be 500+70

Final answer:

To estimate the sum of 503 and 69, one could round the numbers to the nearest tens or hundreds and then add the rounded numbers together. For example, rounding to the nearest tens would result in the equation 500 + 70 = 570.

Explanation:

The question asks for a method to write an equation that would allow them to estimate the sum of 503 and 69. This is more related to the concept of rounding numbers. We can estimate this sum by rounding these numbers to the nearest tens or hundreds, and then adding those rounded numbers together.

For example, if you round to the nearest tens, 503 can be rounded down to 500 and 69 can be rounded up to 70. Adding these rounded numbers together gives 500 + 70 = 570. Therefore, one possible equation could be: 500 + 70 = 570, which is a fairly close estimate of the original sum, 503 + 69.

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A roof rises 9 feet for every 12 feet of run. What is the slope of the roof?

Answers

The slope is 9/12 or 0.75

Since slope, m, is defined as the rise/run; then m = 9/12

simplify m = 3/4

A mother gives birth to a 10 pound baby. Every 4 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.

Answers

10 is b because it stays the same, it is added to the independent variable.

X is the age of the baby in months, but every 4 months so you have to divide and times by two due to the fact that it has to be multiplied by 2. Which leads it to be...

Y= 2x/4+10

Final answer:

The equation of the line that describes the baby's weight is y = (1/2)x + 10.

Explanation:

To find the equation of the line that describes the baby's weight, we need to determine the slope and y-intercept of the line. The slope represents the rate at which the baby's weight increases, and the y-intercept represents the initial weight of the baby.

Since the baby gains 2 pounds every 4 months, the slope of the line is 2/4 = 1/2. This means that for every month that passes, the baby's weight increases by 1/2 pound.

To find the y-intercept, we can use the initial weight of the baby, which is 10 pounds. So the equation of the line is y = (1/2)x + 10.

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A new restaurant is to contain two-seat tables and four-seat tables. Fire codes limit the restaurant's maximum occupancy to 72 customers. If the owners have hired enough servers to handle 22 tables of customers, how many of each kind of table should they purchase?

Answers

Let t and f be the number to two and four seat tables respectively.

t+f=22, solve for t

t=22-f, then we are told that capacity must be less than or equal to 72 people.

2t+4f≤72, using t found above in this equation we get:

2(22-f)+4f≤72 perform indicated multiplication on left side

44-2f+4f≤72 combine like terms on left side

44+2f≤72 subtract 44 from both sides

2f≤28 divide both sides by 2

f≤14 Since f=integer

f=14, and since t=22-f

t=8

So they should purchase 14 four seat tables and 8 two seat tables.

Final answer:

To adhere to the fire code and server capacity, the restaurant should ideally buy 18 four-seat tables and 4 two-seat tables. This results in a total of 22 tables and maximizes seating capacity at 72.

Explanation:

This problem can be solved using a system of linear equations. Let's denote the number of two-seat tables as T and the number of four-seat tables as F.

From the information given, we can establish two equations:

The total number of tables must not exceed 22, so T + F ≤ 22The total number of seats cannot exceed 72, so 2T + 4F ≤ 72

To figure out how many of each type of table they should purchase, we need to solve this system of equations.

The goal is to maximize the number of customers (seats) while not exceeding the limits on tables and seats. So, a possible solution to maximize seating would be to have 18 four-seat tables (F = 18) and 4 two-seat tables (T = 4). This gives a total of 22 tables and 72 seats.

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0.8 is 10 times as great as which decimal

Answers

0.08 is the answer. :)

What is the relationship between the 6s in the number 7,664?

Answers

Answer:

10s

100s

Step-by-step explanation:

One of the 6s are in the 10th digit position

the other one is in the 100th digit position

⦁ The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 ⦁ What is the expected value for each choice? ⦁ Should he pass the ball or take the shot himself? Explain

Answers

Answer:

The given data is

Pr(xi)=0.3*0.70

The expected value =0.90

Where as we calculated the probability=0.96

As 0.96>0.9

So he should pass the ball as probability is greater.

Solve p=10a+3b for a.

Answers

see attached picture for solution

On average, the merchandise shop sells 80 CDs for every 1 vinyl record. Estimate how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs.

Answers

The merchandise shop sells 80 CDs for every 1 vinyl record. We have to find how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs:
         80 CDs -------------------- 1 vinyl record
        760 CDs --------------------- x vinyl records
     ---------------------------------------------------------
        80 : 760 = 1 : x
        80 x = 760
        x = 760 : 80
        x = 9.5 or 9 ( we need a whole number )
       Answer: They are likely to sell 9 vinyl records.

Answer:

10 vinyl records are expected to be sold.

Step-by-step explanation:

On average, the merchandise shop sells 80 CDs per 1 vinyl record. This is our conversion factor. To estimate the number of vinyl records likely to be sold when 760 CDs have been sold we will use proportions.

760 CD × (1 vinyl record/ 80 CD) = 9.5 ≈ 10 (we round it off because you cannot sell half a vinyl record).

10 vinyl records are expected to be sold.

Paige pays $532 per month for 5 years for a car. she made a down payment of $3,700.00. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

Answers

Use the formula of the present value of annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value?
PMT monthly payment 532
R interest rate 0.071
K compounded monthly 12
N time 5years
Pv=532×((1−(1+0.071÷12)^(−12
×5))÷(0.071÷12))
=26,803.15

So the cash price of the car including down payment is
26,803.15+3,700
=30,503.15...answer

A random sample of 12 graduates of a certain secretarial school typed an average of 79.3 words per minute with a standard deviation of 7.8 words per minute. assuming a normal distribution for the number of words typed per minute, find a 95% confidence interval for the average number of words typed by all graduates of this school.

Answers

We will use the following formula to work out the confidence interval

Upper limit = μ + z* (σ/√n)
Lower limit = μ - z* (σ/√n)

We have
μ = 79.3
σ = 7.8
n = 12
z* is the z-score for 95% confidence level = 1.96

Substitute these into the formula, we have

Upper limit = 79.3 + 1.96 (7.8/√12) = 83.7
Lower limit = 79.3 - 1.96 )7.8/√12) = 74.9

Final answer:

To find the 95% confidence interval for the average number of words typed, use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).

Explanation:

To find the 95% confidence interval for the average number of words typed by all graduates of the secretarial school, we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / square root of sample size)

Plugging in the given values, we have:

Confidence Interval = 79.3 ± (1.96) * (7.8 / √12)

Simplifying, the 95% confidence interval is approximately 75.6 to 83.0 words per minute.

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Find the surface area of a cylinder with a diameter of 2 and an altitude of 16

Answers

The surface area of the cylinder is given by:
S.A=2πr^2+πdl
hence, the s.a of our solid will be:
S.A.=2*π*1^2+π*2*16
=6.283+100.531
=106.814 sq. units

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The following table shows the probability distribution for a discrete random variable. X 13| 16 |17| 21| 23| 25 |26 |31 P(X) 0.07 |0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08 What is the mean of this discrete random variable. That is, what is E(X), the expected value of X?

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The following table shows the probability distribution for a discrete random variable.
X 13| 16 |17| 21| 23| 25 |26 |31
P(X) 0.07 |0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08
What is the mean of this discrete random variable. That is, what is E(X), the expected value of X?