38â% 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 partsâ (a) throughâ (d) below.(a) Find the mean of the binomial distribution. μequals= ( ) (Round to the nearest tenth asâ needed.) â
(b) Find the variance of the binomial distribution.
sigmasquared= ( ) â(Round to the nearest tenth asâ needed.)
â(c) Find the standard deviation of the binomial distribution.
sigma = ( ) (Round to the nearest tenth asâ needed.) â
(d) Interpret the results in the context of theâ real-life situation.
Onâ average ( ) out of 6 women would consider themselves baseball fans. The standard deviation is ( ) âwomen, so in most samples of 6â women, the number of women who consider themselves baseball fans would differ from the mean by no more than ( ).â(Type integers or decimals rounded to the nearest tenth asâneeded.)

a) 2.3

b) 1.4

c) 1.2

d) On average, 2.3 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.

Step-by-step explanation:

For each woman, there are only two possible outcoes. Either they are a fan of professional baseball, or they are not. The prbability of a woman being a fan of professional baseball is independent of other woman. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The variance of the binomial distribution is:

The standard deviation of the binomial distribution is:

38% of women consider themselves fans of professional baseball.

This means that

Six women are sampled:

This means that

(a) Find the mean of the binomial distribution.

(b) Find the variance of the binomial distribution

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

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

On average, 2.3 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.

nothjing

step-by-step explanation: