Between 32 and 34 Hours

D

z = (x-u)/sigma. z1 = 32 - 32/2 = 0 and z2 = 34 - 32/2 = 1. From the z tables, z = 0 and z = 1 are 0 and 0.3413 respectively. Therefore, the area under the curve is

0.3413.

To solve this question, we can use the properties of the normal distribution and z-scores.

Given: Mean (μ) = 32 hours Standard Deviation (σ) = 2 hours

We want to find the percentage of garages that take between 32 and 34 hours to erect. In other words, we need to find the area under the normal distribution curve between these two values.

First, we need to calculate the z-scores for these two values using the formula:

z = (x - μ) / σ

For 32 hours: z1 = (32 - 32) / 2 = 0

For 34 hours: z2 = (34 - 32) / 2 = 1

Now, we can use the z-scores to find the area under the normal distribution curve between these two values. We can use a standard normal distribution table or a calculator to find this area.

Looking up the z-scores in a standard normal distribution table, we can find the corresponding probabilities:

For z = 0, the corresponding probability is 0.5000. For z = 1, the corresponding probability is 0.8413.

To find the area between these two z-scores, we subtract the probability corresponding to z1 from the probability corresponding to z2:

Area = P(z1 ≤ z ≤ z2) = P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0) = 0.8413 - 0.5000 = 0.3413

This means that 34.13% of the garages take between 32 and 34 hours to erect.

Therefore, the correct answer is D. 34.13%.