Question

A certain population of children has height thus have a Normal Distribution with a mean of 40.8 inches and standard deviation of 2.4 inches.

a) if 36 perosns are randomly selected from this population, find the probability that thieir mean height is at most 39 inches. Draw a good diagram to support your answer and show the z-score.

Answer 1

MEAN= 40.8 inches and Standard deviation = 2.4 inches

For n=36

Standard error of mean= 2.4/sqrt(36)= 2.4/6= 0.4

=

P ( X<39 )=P ( X−μ<39−40.8 )=P ((Xbar−μ)/s.e<(39−40.8)/0.4)

Since (xbar−μ)/s.e=Z and (39−40.8)/0.4=−4.5 we have:

P (Xbar<39)=P (Z<−4.5)

Use the standard normal table to conclude that:

P (Z<−4.5)=0.000