SOLUTION: 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 standa

Question 135562: 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 percent take how many hours or more to erect?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
P(32 < x <34) = P(0 < z < 1)=0.3413
-------------------------------
b. What percent of the garages take between 29 hours and 34 hours to erect?
P(29 < x <34) = P (-1.5 < z < 0)=0.4332
--------------------------------------
c. What percent of the garages take 28.7 hours or less to erect?
P(0 < x < 28.7) = P(-16 < x < -1.65) = 0.0495
--------------------------------------------
d. Of the garages, 5 percent take how many hours or more to erect?
Find the z-score associated with the upper 5%: z=1.645
Find the corresponding x-score using z=(x-u)/s
1.645 = (x-32)2
x-32 = 2*1.645
x = 3.290+32 = 35.29 hours
===============================
Cheers,
Stan H.

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