Question

6.2.38 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. (Use Minitab where applicable.)

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

b.         What is the probability that more than 6 weigh more than 20 pounds?

c.         What is the probability that fewer than 3 weigh more than 20 pounds?

d.         Would it be unusual if more than 8 of them weigh more than 20 pounds?

e.         What is the mean number who weigh more than 20 pounds in a sample of 16 babies aged 6-8 months?

f.          What is the standard deviation of the number who weigh more than 20 pounds in a sample of 16 babies ages 6-8 months?

Answer 1

X ~ B ( n = 16 , P = 0.25 )

Part a)

Part b)

P ( X > 6 ) = 1 - P ( X <= 6 )

P ( X > 6 ) = 0.0795

Part c)

P ( X < 3 ) = 0.1971

Part d)

P ( X > 8 )

P ( X > 8 ) = 0.0074

Yes, it is unusual because the probability is less than 5% i.e < 0.05

Part e)

Mean = n * P = ( 16 * 0.25 ) = 4

part f)

Variance = n * P * Q = ( 16 * 0.25 * 0.75 ) = 3
Standard deviation = (variance) = (3) = 1.7321