A small engine shop receives an average of repair calls per​ hour, with a standard deviation of . What is the mean and standard deviation of the number of calls it receives for ​-hour ​day? What, if​ anything, did you​ assume?

Assuming normal distribution, the mean number of calls for a n-hour day is of , in which is the mean number of calls per hour, and the standard deviation is , in which is the standard deviation of the number of calls per hour.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

N-instances of a normal variable:

For n-instances of normal variable, the mean of the distribution is: , and the standard deviation is

What is the mean and standard deviation of the number of calls it receives for ​n-hour ​day?

Assuming normal distribution, the mean number of calls for a n-hour day is of , in which is the mean number of calls per hour, and the standard deviation is , in which is the standard deviation of the number of calls per hour.

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