Question

The heights for 5-year-old boys follow the normal distribution with a mean height of 43 inches and a standard deviation of 5.3 inches. A sample of 60 boys is randomly selected.If possible, find the probability that the mean height of boys in the sample is higher than 42 inches. If not, explain.

Answer 1

= 43 inches

= 5.3 inches

For sampling distribution of mean for a sample of size n,

P( < A) = P(Z < (A - )/)

n = 60

= = 43 inches

=

=

= 0.6842

P(mean height of boys in the sample is higher than 42 inches) = P( > 42)

= 1 - P( < 42)

= 1 - P(Z < (42 - 43)/0.6842)

= 1 - P(Z < -1.46)

= 1 - 0.0721

= 0.9279