Question

A national manufacturer of unattached garages discovered thatthe distribution of the lengths of time it takes two constructionworkers to erect the Red Barn model is aproximately normallydistributed with a mean of 32 hours and a standard deviation of 2hours.

What percentage of the garages take between 30 and 34hours to erect?
A. 16.29%
B. 76.71%
C. 3.14%
D. 68.00%

Answer 1

D. 68.00%

Explanation:

Population mean time (μ) = 32 hours

Standard deviation (σ) = 2 hours

Assuming a normal distribution, for any given number of hours 'X', the z-score is determined by:

`z=(X-\mu)/(\sigma)`

For X=30

`z=(30-32)/(2)\\z=-1`

For a z-score of -1, 'X' corresponds to the 15.87-th percentile of a normal distribution.

For X=34

`z=(34-32)/(2)\\z=1`

For a z-score of 1, 'X' corresponds to the 84.13-th percentile of a normal distribution.

The percentage of the garages that take between 30 and 34 hours to erect is:

`P(30 \leq X \leq 34) = 84.13\% - 15.87\%= 68.3\%`

The percentage is roughly 68%.