A 1994 report revealed that 326 of US births were to unmarri

A 1994 report revealed that 32.6% of U.S. births were to unmarried women. A parenting magazine selected 30 women who gave birth in 1994 at random. What is the probability that exactly 10 of the women were unmarried? Using your calculator determine the probability that in the sample at most 10 are unmarried.

Solution

p=0.326

n=30

Binomial distribution used.

P(X=x) = (_nC_x) p^x (1-p)^n-x   

a).

P(X=10) = (₃₀C₁₀) 0.326¹⁰ (1-0.326)^30-10   

P(X =10) = 0.1525

b).

P( at most 10) = P( x 10)

= 0.6182