Question

Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days.

Answer 1

We should request a completion time of

223 work-days.

Answer 2

Answer:

233 days.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 200, \sigma = 10$

To be 99% sure that we will not be late in completing the project, we should request a completion time of ...

This is the value of X when Z has a pvalue of 0.99. So X when Z = 2.325.

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

$2.325 = \frac{X - 200}{10}$

$X - 200 = 10*2.325$

$X = 232.5$

So the correct answer is 233 days.