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 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow normal distribution

a. determine the z values for 29 and 39 hours. what percent of the garages take between 32 and 34 hours to erect?

b. what percent of the garages take between 29 and 24 hours to erect?

c. What percent of the garages take 28.7 hours to erect?

d of the garages, 5 percent take how many hours or more to erect?

Explanation / Answer

Solution:

z = (X - ) / x

Where X is a normal random variable, is the mean, and is the standard deviation.

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

z29 = (29-32)/2 = -1.5
z34 = (34-32)/2 = 1

What percent of the garages take between 32 hours and 34 hours to erect?
Using the calculator at site http://davidmlane.com/hyperstat/z_table.html gives
p(0 < z < 1) = 0.3413 = 34.13% (answer)


b. What percent of the garages take between 29 hours and 34 hours to erect?
Using the calculator at site http://davidmlane.com/hyperstat/z_table.html gives
p(-1.5 < z < 1) = 0.7745 = 77.45%

c. What percent of the garages take 28.7 hours or less to erect?
Calculation of z = (28.7-32)/2 = -1.65

Using the calculator at site http://davidmlane.com/hyperstat/z_table.html gives
p(z < -1.65) = 0.0495 = 4.95%

d. Of the garages, 5 percent take how many hours or more to erect?
Here significance level is 0.05,

So, z0.05 = 1.645 [critical value](Using Statistical Ratio Calculator

From http://www.graphpad.com/quickcalcs/DistMenu.cfm for calculating z with 0.05 significance)

Now, 1.645 = (x-32)/2
=> x = 35.29 hours (answer)

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