He length of time to perform an oil change at a certain automobile repair shop is ap-proximately normally distributed with mean 29.5 minutes and standard deviation 3 minutes. What is the probability that a mechanic can complete 16 oil changes in an eight-hour day

56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day

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 that a mechanic can complete 16 oil changes in an eight-hour day

16 oil changes in 8 hours is 2 changes per hour, that is, one each 30 minutes.

This probability is the pvalue of Z when X = 30. So

has a pvalue of 0.5675

56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day