Question

3737​%

of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball. Complete parts​ (a) through​ (c) below.​(a) Construct a binomial distribution using

n equals 6n=6

and

p equals 0.37p=0.37.

x	​P(x)
0	0.0630.063
1	0.2200.220
2	0.3230.323
3	0.2530.253
4	0.1120.112
5	0.0260.026
6	0.0030.003

​(Round to the nearest thousandth as​ needed.)

​(b) Graph the binomial distribution using a histogram and describe its shape. Choose the correct graph below.

A.

024600.050.10.150.20.250.30.350.4xP(x)

A histogram has a horizontal axis labeled x from 0 to 7 in increments of 1 and a vertical axis labeled P(x) from 0 to 0.4 in increments of 0.05. The histogram has vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: 0, 0.003; 1, 0.026; 2, 0.112; 3, 0.253; 4, 0.323; 5, 0.220; 6, 0.063.

B.

024600.050.10.150.20.250.30.350.4xP(x)

A histogram has a horizontal axis labeled x from 0 to 7 in increments of 1 and a vertical axis labeled P(x) from 0 to 0.4 in increments of 0.05. The histogram has vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: 0, 0.003; 1, 0.026; 2, 0.063; 3, 0.112; 4, 0.253; 5, 0.323; 6, 0.220.

C.

024600.050.10.150.20.250.30.350.4xP(x)

A histogram has a horizontal axis labeled x from 0 to 7 in increments of 1 and a vertical axis labeled P(x) from 0 to 0.4 in increments of 0.05. The histogram has vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: 0, 0.063; 1, 0.220; 2, 0.323; 3, 0.253; 4, 0.112; 5, 0.026; 6, 0.003.This is the correct answer.

D.

024600.050.10.150.20.250.30.350.4xP(x)

A histogram has a horizontal axis labeled x from 0 to 7 in increments of 1 and a vertical axis labeled P(x) from 0 to 0.4 in increments of 0.05. The histogram has vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: 0, 0.063; 1, 0.323; 2, 0.220; 3, 0.253; 4, 0.112; 5, 0.026; 6, 0.003.Your answer is not correct.

Describe the shape of the histogram. Choose the correct answer below.

A.

Symmetrical

B.

Skewed right

Your answer is correct.

C.

Skewed left

D.

None of these

​(c) What values of the random variables would you consider​ unusual? Explain your reasoning.

On​ average,

nothing

out of 6 women would consider themselves baseball​ fans, with a standard deviation of

nothing

women. The values

x equals 6x=6

and

xequals=nothing

would be unusual because their probabilities are

▼

less than

equal to

greater than

0.05.

​(Round to the nearest tenth as​ needed.)

Enter your answer in the edit fields and then click Check Answer.

Answer 1

(b)

Following is the histogram:

The distribution skewed to right. It is not symmetric.

The mean is

(b)

The variance is

The standard deviation is

On average, 2.2 out of 6 women would consider themselves baseball fans. The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 2*1.2 = 2.4.

----------------------------

The range of unusual values are

On​ average,2.2bout of 6 women would consider themselves baseball​ fans, with a standard deviation of 1.2 women. The values x =0

and x = 4.6 would be unusual because their probabilities are less than 0.05.