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 assembley 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?
The z value for 29 is (29-32)/2 = -1.5
The z value for 34 is (34-32)/2 = 1.0
The probability for 32 to 34 is 34.1%
I used the graphical tool at http://psych-www.colorado.edu/~mcclella/java/normal/accurateNormal.html to get that last result
the accontieg depatment at
To solve this problem, we need to use the concept of z-scores and the standard normal distribution.
Step 1: Calculate the z-scores
The formula to calculate the z-score is given by:
z = (x - μ) / σ
where:
- x is the given value,
- μ is the mean, and
- σ is the standard deviation.
For 29 hours:
z = (29 - 32) / 2 = -1.5
For 34 hours:
z = (34 - 32) / 2 = 1
Step 2: Find the percentage of garages that take between 32 and 34 hours to erect.
To find the percentage, we need to look up the z-scores in the standard normal distribution table or use a calculator.
From the z-score table, we can find that the area to the left of -1.5 is approximately 0.0668, and the area to the left of 1 is approximately 0.8413.
Now, to find the percentage between 32 hours and 34 hours, we subtract the area to the left of 32 hours from the area to the left of 34 hours.
Thus, the percentage is approximately 0.8413 - 0.0668 = 0.7745, or 77.45%.
So, approximately 77.45% of the garages take between 32 hours and 34 hours to erect.