Question

The accounting department at Weston Materials Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to build the Red Barn model. Assume the assembly times follow the normal distribution.

a. Determine the z-values for 29 and 34 hours.

b. What percentage of the garages take between 32 hours and 34 hours to build?

c. What percentage of the garages take 28.7 hours or less to build?

d. What percentage of the garages take 35.5 hours or more to build?

I want the answer to be solved in excel

Answer 1

a)

z-score = (X - mean) / SD

For X = 29 ,

z = ( 29 - 32) / 2

= -1.5

For X = 34

z = (34 -32) / 2

= 1

b)

P(32 <X < 34) = P(X < 34) - P(X < 32)

= NORM.DIST(x , mean, SD , cumulative)

= NORM.DIST( 34 , 32 , 2 , TRUE) - NORM.DIST( 32 , 32 , 2 , TRUE)

= 0.8413 - 0.5

= 0.3413

= 34.13%

C)

P(X < 28.7) = NORM.DIST( 28.7 , 32 , 2 , TRUE)

= 0.0495

= 4.95%

d)

P(X > 35.5) = 1 - P(X < 35.5)

= 1 - NORM.DIST( 35.5 , 32 , 2 , TRUE)

= 1 - 0.9599

= 0.0401

= 4.01 %