# Probabilities, Hypothesis Testing

Part 2. Evaluate probabilities using the laws of probability, the standard normal distribution, t-distribution, or X2-distribution.

Mike's Ice Cream shop sells ice cream and related products. Past experience indicates that the daily sales follow a probability distribution that has a mean of $1000 and a standard deviation of $300. What is the probability that a randomly selected sample of seven days, the daily sales will have a mean of at most $880?

Show all steps to your calculations.

Part 3: Use hypothesis testing to investigate claims involving one or two samples, utilizing the standard normal distribution, t-distribution, r-distribution, and X2-distribution.

Each of a random sample of ten college freshmen takes a mathematics aptitude test both before and after undergoing an intensive training course designed to improve such test scores. Then the scores for each student are paired, as shown in the table.

Student Before After

1 60 70

2 73 80

3 42 48

4 88 94

5 66 79

6 77 86

7 90 93

8 63 71

9 55 70

10 96 97

Test the claim that the training course improves the test scores at the 5% significance level. Show all steps in your test of the claim.

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#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.