Question

Tompkins Associates reports that the mean clear height for a Class A warehouse in the United States is 22 feet. Suppose clear heights are normally distributed and that the standard deviation is 4 feet. A Class A warehouse in the United States is randomly selected.

(a) What is the probability that the clear height is greater than 16 feet?
(b) What is the probability that the clear height is less than 11 feet?
(c) What is the probability that the clear height is between 24 and 30 feet?

Answer 1

Mean = 22

Standard Deviation = 4

a)

P( X > 16)

Z score at X =16

Z = (X - ?) / ?
Z = (16 - 22) / 4

Z = -1.5

From Z score table

P(X > 16) = P( Z > -1.5) = 0.9332

b)

P( X < 11)

Z score at x=11

Z = (X - ?) / ?
Z = (11 - 22) / 4

Z = -2.75

From Z score table

P( X < 11) = P( Z < -2.75) = 0.003

c)

P( 24 < x < 30)

Z score at X = 24

Z = (X - ?) / ?
Z = (24 - 22) / 4

Z = 0.5

Z score at X = 30

Z = (X - ?) / ?
Z = (30 - 22) / 4

Z = 2

From Z score table

P( 24 < X < 30) = P( 0.5 < Z < 2) = 0.2858