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. (b) find the variance of the binomial distribution. (c) Find the standard deviation of the binomial distribution

Answer:

(a) 2.22

(b) 1.3986

(c) 1.183

Step-by-step explanation:

Let X denote the number of women who consider themselves fans of professional baseball.

The proportion of women who consider themselves fans of professional baseball is, p = 0.37.

A random sample of n = 6 women are selected and each was asked if she considers herself a fan of professional baseball.

Each woman's reply is independent of the others.

The random variable X thus follows a binomial distribution with parameters n = 6 and p = 0.37.

(a)

Compute the mean of the binomial distribution as follows:

[tex]\text{Mean}=np=6\times 0.37=2.22[/tex]

(b)

Compute the variance of the binomial distribution as follows:

[tex]\text{Variance}=np(1-p)=6\times 0.37\times (1-0.37)=1.3986[/tex]

(c)

Compute the standard deviation of the binomial distribution as follows:

[tex]\text{Standard Deviation}=\sqrt{np(1-p)}=\sqrt{6\times 0.37\times (1-0.37)}=1.183[/tex]

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