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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 200, \sigma = 10[/tex]
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.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.325 = \frac{X - 200}{10}[/tex]
[tex]X - 200 = 10*2.325[/tex]
[tex]X = 232.5[/tex]
So the correct answer is 233 days.
