Question

Suppose that the mean height of all 6th graders is 46 inches with a standard deviation of 2.5 inches. It is reasonable to assume that these heights are normally distributed. Find the percentage of 6th graders who are under 47 inches tall. (round to three decimal places)

Answer 1

Solution:

Given: X = The  height of all 6th graders follows Normal distribution with mean = inches and a standard deviation = inches.

Find:

P( X < 47 ) =...........?

Find z score for x = 47

Thus we get:

Use following Excel command:

=NORM.S.DIST(z,cumulative)

=NORM.S.DIST(0.40,TRUE)

=0.65542

=65.542%

thus we get:

Thus 65.542% of 6th graders who are under 47 inches tall.