Question

The Binomial distribution: Each newborn baby has a probability of approximately 0.54 of being male. For a family with six children, let X=number of children who are girls.

·Identify n and p for the binomial distribution.

·Find the probability distribution of ?

·Find the mean and standard deviation of distribution of ?

Answer 1

Given:

X = number of children who are girl

Each newborn baby has a probability of approximately 0.54 of being male

Therefore, probability for female is 1 - 0.54 = 0.46

For a family with SIX children, i.e. n = 6

a) Identify n and p for the binomial distribution.

n = 6

p = 1 - 0.54 = 0.46

b) Find the probability distribution of X: For Binomial Distribution

................X = 0,1,2,3,4............................n

P(X-z) C * 0.46x * 0.546-x)

C) Find the mean and standard deviation of distribution of X:

Mean = np = 6 * 0.46 = 2.76

SD =

SD V/np * (1-p) V/6 * 0.46 * (1-0.46) = V6 * 0.46 * 0.54 = 1.22