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.)

A) 84.13%

B) 0.3%

C) 38.91%

Step-by-step explanation:

We standardize the values of x by using the formula  

where  

is the mean = 22 feet

is the standard deviation = 4 feet

By doing this, we transform the original distribution too the normal distribution N(0;1) and we can compute the probabilities easily by looking up at tables or by using the computer

A)

for x = 18  

So P(x > 18) = P(z > -1) = 0.8413 or 84.13%

B)

In this case, since a height cannot be negative, we really want

P(0 < x < 11)

for x= 0 and x = 11, z = -5 and z = -2.75 and

P(0 < x < 11) = P(-5 < z < -2.75) = 0.003 = 0.3%

C)

For x = 23 and x = 31, z = 0.25 and z = 2.25 and

step-by-step :