Question

*4.2.27

37

​%

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​ (d) below.

​(a) Find the mean of the binomial distribution.

mu

equals2.2

  

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

​(b) Find the variance of the binomial distribution.

sigma

squaredequals1.4

  

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

​(c) Find the standard deviation of the binomial distribution.

sigma

equals1.2

  

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

​(d) Interpret the results in the context of the​ real-life situation.

On​ average ?

out of 6 women would consider themselves baseball fans. The standard deviation is

?

​women, so in most samples of ?​ women, the number of women who consider themselves baseball fans would differ from the mean by no more than

2

.

​(Type integers or decimals rounded to the nearest tenth as​ needed.)

Answer 1

We have been provided with the following information:

p = probability that women consider themselves fans of professional baseball = 0.37

n = The number of trials = 6

Let X be the number of women out of 6 who are fans of baseball. Then :

(a)

(b)

(c)

(d)

On​ average 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 1.2

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