36 The accounting department at Weston Materials Inc a natio

36. 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 erect the Red Barn model. Assume the assembly times Follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? b. What percent of the garages take between 29 hours and 34 hours to erect? c. What percent of the garages take 28.7 hours or less to erect? d. Of the garages, 5% take how many hours or more to erect?

Solution

Given X~Normal(mean=32, s=2) ------------------------------------------------------------------------------------------ a. Determine the z values for 29 and 34 hours. Z=(X-mean)/s (29-32)/2= -1.5 (34-32)/2=1 ------------------------------------------------------------------------------------------ b. What percent of the garages take between 29 hours and 34 hours to erect? P(29 P(Z<(c-32)/2)=0.05 --> (c-32)/2=-1.645 (check standard normal table) --> c= 32 -1.645*2= 28.71