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

Answer:

D. 68.00%

Step-by-step 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:

$z=\frac{X-\mu}{\sigma}$

For X=30

$z=\frac{30-32}{2}\\z=-1$

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

For X=34

$z=\frac{34-32}{2}\\z=1$

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%.