Big babies: The Centers for Disease Control and Prevention reports that 25% of baby boys 6–8 months old in the United States weigh more than 20 pounds. A sample of 16 babies is studied.

Question

a.	What is the probability that exactly 5 of them weigh more than 20 pounds?

Answer 1

This is a binomial probability problem. Using the binomial formula (and n = 16, k = 5, and p = 0.25), P(5)=C(16,5)*(0.25)^5*(1-0.25)^(16-5), where C(16,5) is number of combinations of 16 choose 5 which equals 16!/(5!*(16-5)!)

Answer 2

Assuming all 16 babies selected for the study are boys of 6 to 8 month of age, this problem will be solved easily with a Bernoulli distribution:

Probability of success: p = 0.25

Total number of trials: n = 16

Number of success: x = 5

P = C(n,x) p^x (1-p)^(n-x)

P = 16!/(5!*11!) * (0.25)⁵ * (0.75)¹¹ = 0.18