Answer the question on Probability and perform a One Sample Hypothesis Test. 

For the Hypothesis Test, make sure to report the following steps:

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.

2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

3. Find the critical value(s) and identify the rejection region(s).

4. Find the appropriate standardized test statistic. If convenient, use technology.

5. Decide whether to reject or fail to reject the null hypothesis.

6. Interpret the decision in the context of the original claim.

Let X be a normal random variable with parameters ?= 8 and jQuery2000003867401856504582_1505410401839?? = 3.5. Find the following probabilities.

1. p(x < 3)

2. p(x > 11)

3. p(3 < x < 11.5)

A sample of 40 IWU freshmen had a mean GPA of 2.8 over all their courses taken in their first semester at IWU. This sample had a standard deviation of .25. Perform a hypothesis test at ? = 0.05 to determine if the first semester GPA of all IWU freshmen is less than a B (3.0).

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