The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that is 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 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?

Z = (x-mean)/SD

Calculate the Z scores for the values above. Look them up in a table in the back of your stat text labeled something like "areas under the normal distribution." Find the proportions between or beyond the indicated values and convert to percentages.

I hope this helps.

To answer these questions, we will use the concept of z-scores and the standard normal distribution.

a. To determine the Z-values for 29 and 34 hours, we need to calculate the z-scores using the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation.

For 29 hours:
Z1 = (29 - 32) / 2 = -1.5

For 34 hours:
Z2 = (34 - 32) / 2 = 1

To find the percentage of garages that take between 32 and 34 hours to erect, we need to find the area under the standard normal curve between these two z-scores. We can use a standard normal distribution table or a statistical calculator to find the corresponding probabilities.

Using the standard normal distribution table, we find that the area to the left of -1.5 is 0.0668 and the area to the left of 1 is 0.8413. Therefore, the area between these two z-scores is:

Area = 0.8413 - 0.0668 = 0.7745

So, the percentage of garages that take between 32 and 34 hours to erect is 77.45%.

b. To find the percentage of garages that take between 29 and 34 hours to erect, we need to find the area under the standard normal curve between the z-scores corresponding to these times.

Using the standard normal distribution table, we find that the area to the left of -1.5 is 0.0668 and the area to the left of 1 is 0.8413. Therefore, the area between these two z-scores is:

Area = 0.8413 - 0.0668 = 0.7745

So, the percentage of garages that take between 29 and 34 hours to erect is 77.45%.

c. To find the percentage of garages that take 28.7 hours or less to erect, we need to find the area under the standard normal curve to the left of the corresponding z-score.

Using the z-score formula, we can calculate the z-score for 28.7 hours:

Z = (28.7 - 32) / 2 = -1.65

Using the standard normal distribution table, we find that the area to the left of -1.65 is 0.0495.

So, the percentage of garages that take 28.7 hours or less to erect is 4.95%.

d. To find the number of hours that 5% of garages take or more to erect, we need to find the corresponding z-score from the standard normal distribution table.

Using the table, we find the z-score corresponding to an area of 0.95 (since we want the area to the right of the z-score) is approximately 1.645.

Now we can use the formula Z = (X - μ) / σ to find the corresponding X value:

1.645 = (X - 32) / 2

Solving for X, we get:

X = 1.645 * 2 + 32 = 35.29

So, 5% of the garages take 35.29 hours or more to erect.