# Determining Probability For a Normal Random Variable

To decrease the amount of time it takes to deliver packages, a delivery company purchased computer software that finds the optimal route for making deliveries based upon the input of the package destinations. In the past the average amount of time it took to complete deliveries was 9.4 hours with a standard deviation of 0.8 hours. Since purchasing the software the average delivery time over twenty delivery days was 8.6 hours. At the 0.05 level of significance, test whether the software package has reduced the average time it takes to complete deliveries.

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#### Solution Preview

Let mu be the mean time that it takes to complete deliveries, we want to test ...

#### Solution Summary

The solution gives detailed steps on performing the hypothesis tesing assuming the data is normally distribution. Both population mean and standard deviation are given in the question.

Determining Probability of Random Variable: Example Problem

Find the probability that a standard normal random variable will assume a value between:

a. z = 1.5 and z = .75

b. Greater than 1.25

c. Find a z such that 70% of the area is above that value.