1. A standardized test is normally distributed with a mean of 100 and a standard deviation of 10.

A. Find the probability that a randomly selected student scores between a 90 and 100.

B. Suppose we take a sample of 100 students and we want to know the probability that the mean of that sample is between 90 and 100. Is this probability the same as the probability we found in A? Why or why not? Explain using complete sentences.

2. In the NFL, the football should be inflated to 12.5 pounds per square inch (PSI). In the 2015 AFC championship game there was controversy as the New England Patriots were accused of deflating footballs to make it easier for their players to grip. 11 Footballs were collected and the PSI's for each football were recorded:

11.510.8511.1510.7011.1011.6011.8511.1010.9510.5010.90

Run a hypothesis test with significance level , to determine whether there is sufficient evidence to say the Patriots deflated footballs.

A) State the null and alternative hypothesis.

B) State the test statistic (include the appropriate letter) and the p-value.

C) What is the test decision?

D) Note a conclusion using complete sentences.