A project has a mean completion time of 54 weeks and a standard deviation of the project completion time of 2.95 weeks. What is the probability of completing the project within 52 weeks? Please put your answer in terms of a probability (i. e. a number between 0 and 1), and not a percentage.

0.2483

Step-by-step explanation:

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

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

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:

What is the probability of completing the project within 52 weeks?

This is the pvalue of Z when X = 52.

has a pvalue of 0.2483

So the answer is 0.2483

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.