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# Random variables, Expected Values, Chi-Square and Levels of Significance

Question 8: In business, time is money. A local entrepreneur wants to start a regional 24/7 package delivery service for businesses along the front range. A key planning assumption is that, with Colorado Springs as the collection and distribution hub, package delivery times throughout this region will follow a Normal Probability Distribution. Using US Postal Service data and other information, an analyst constructs the following projected package delivery times (in hours) for the front range region:

Hours Frequency

1 up to 3* 4
3 up to 5 12
5 up to 7 21
7 up to 9 30
9 up to 11 25
11 up to 13 8

* Recall that "up to 3" doesn't include 3.
Given the hypotheses: H0: The package delivery time is approximately Normal**
H1: The package delivery time is not approximately Normal

** "Normal" means that the Normal Probability Distribution is followed.

a. What is the random variable for this problem.

b. Using Expected Value, find the mean and standard deviation for the information given.

c. Using the 0.01 level of significance and a Chi Square Goodness of Fit test, state your conclusion as to whether the package delivery times, in hours, are Normally distributed (follow the Normal pattern).

keywords: chi-squared, squared

#### Solution Summary

Random variables, Expected Values, Chi-Square and Levels of Significance are investigated.

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