Tompkins Associates reports that the mean clear height for a Class A warehouse i
ID: 3160010 • Letter: T
Question
Tompkins Associates reports that the mean clear height for a Class A warehouse in the United Statesis 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 18 feet? P(x>18) = 0.8413
B) What is the probability that the clear height is less than 11 feet? P(x<11) = ???
C) What is the probability that the clear height is between 23 and 31 feet? P(23<= x <= 31) = ???
(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)
Explanation / Answer
Normal Distribution
Mean ( u ) =22
Standard Deviation ( sd )=4
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X > 18) = (18-22)/4
= -4/4 = -1
= P ( Z >-1) From Standard Normal Table
= 0.8413
b.
P(X < 11) = (11-22)/4
= -11/4= -2.75
= P ( Z <-2.75) From Standard Normal Table
= 0.003
c.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 23) = (23-22)/4
= 1/4 = 0.25
= P ( Z <0.25) From Standard Normal Table
= 0.59871
P(X < 31) = (31-22)/4
= 9/4 = 2.25
= P ( Z <2.25) From Standard Normal Table
= 0.98778
P(23 < X < 31) = 0.98778-0.59871 = 0.3891