The accounting department at Weston Materials Inc., a national manufacturer of u

Question

The accounting department at Weston Materials Inc., a national manufacturer of unattached garages reports that it takes two construction workers a mean of 49 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. Refer to the table ir Appendix B.1 a-1. Determine the z-values for 47 and 53 hours. (Negative answers should be indicated by a minus sign. Round the final answers to 1 decimal place. 47 hours corresponds to z = 53 hours corresponds to z = What percentage of the garages take between 49 hours and 53 hours to erect? (Round the final 8413 lo.gm2 a-2. answer to 2 decimal places.) Percentage 9% b. What percentage of the garages take between 47 hours and 53 hours to erect? (Round the final answer to 2 decimal places.) Percentage c. What percentage of the garages take 46.2 hours or less to erect? (Round the final answer to 2 decimal places.) Percentage d. Of the garages, 10% take how many hours or more to erect? (Round the final answer to 1 decimal place.) Hours

Explanation / Answer

a-2. z(49) = z(49-49/2) = 0, z(53)= 53 - 49/2 = 2

P(49 < x < 53) = P(0 < z < 2) = 0.4772 = 47.72%

b.   z(47) =   47- 49/2 = -1 and z(53) = 53-49/2 = 2

P(47 < x <53) = P( -1 < z < 2) =   0.3413 to 0.4772 = 0.8185 = 81.85%

c.   z(46.2) =   (46.2 - 49)/2 = 2.8

for the z table the percentage of garages take 46.2 hours or less to erect = 0.0026 = 0.26%

d. Use the z-chart or InvNor(0.90) = 1.29

x value corresponding to z value 1.282 = x - 49/ 2

x - 49 = 1.282 X 2

x-49 = 2.564

x = 2.564 + 49 = 51.564 hours

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