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 14 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 23 and 30 feet?

Answer 1

Solution :

Given that,

mean = = 22

standard deviation = = 4

a ) P (x > 14 )

= 1 - P (x < 14)

= 1 - P ( x -  / ) < ( 14 - 22 / 4)

= 1 - P ( z <- 8 / 4 )

= 1 - P ( z < - 2)

Using z table

= 1 - 0.0228

= 0.9772

Probability = 0.9772

b ) P( x < 11 )

P ( x - / ) < ( 11 - 22 / 4)

P ( z < -11 / 4 )

P ( z < -2.75)

= 0.0030

Probability = 0.0030

c ) P (23 < x < 30 )

P ( 23 - 22 / 4) < ( x -  / ) < ( 30 - 22 /4)

P ( 1 / 2< z < 8 / 4 )

P (1 < z < 2 )

P ( z < 2 ) - P ( z < 0.25)

Using z table

= 0.9772 - 0.5987

= 0.3785

Probability = 0.3785