Problems You will complete a question onProbabilityand perform aOne Sample Hypothesis Test. For theHypothesis 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 = 3.5. Find the following probabilities.

Resource: Finding Normal Probability

1. p(x < 5)
2. p(x > 10)
3. p(6 < x < 12)

• A production line produces rulers that are supposed to be 12 inches long. A sample of 49 of the rulers had a mean length of 12.1 inches and a standard deviation of .5 inches. The quality control specialist responsible for the production line wants to determine whether the production line is really producing rulers that are 12 inches long or not. Perform a hypothesis test at = 0.10.