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]
