Question

36 % of men think of themselves fans of professional baseball. You randomly select six men and ask each if he considers himself 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) come up with the standard deviation of the binomial distribution.

(d) Interpret the end result in the context of the real-life situation.

Answer 1

(a)

Binomial Distribution

n = 6

p = 0.36

q = 1 - p = 0.64

Mean of the Binomial Distribution is given by:

= np = 6 X 0.36 = 2.16

So,

Mean = 2.16

(b)

Variance of Binomial Distribution is given by:

= npq = 6 X 0.36 X 0.64 = 1.3824

So,

Variance = 1.3824

(c)

Standard deviation of Binomial Distribution is given by:

So,

Standard Deviation = 1.1758

(d) Interpretation:

Out of 6 men selected, we can expect around 2 persons to be a fan of professional baseball with a variation of around 1.