1. IQ tests are standardized and follow a normal distribution. On a common IQ test, the mean score is 100 with a standard deviation of 15. a) What is the probability that a randomly selected individual gets a score of 105 or higher? b) What are the mean and standard deviation of the average score of an SRS of 50 people? (Don't forget to justify this.) c) What is the probability that the average score of an SRS of 50 people is 105 or higher?

2. Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B? Be sure to state and justify your assumptions.

3. An opinion poll asks an SRS of 1500 adults, "Do you happen to jog?" Suppose that the population proportion who jog (a parameter) is p = 0.15. To estimate p, you use the proportion p-hat in the sample who answer "Yes." Justify the use of a normal approximation and find the following probabilities. a) P(p > 0.16) b) P(0.14

4. The distribution of salaries in a company is skewed to the right. That is, most employees make a small amount of money while a few executives earn much higher salaries. a) What would a sampling distribution of sample size 3 look like? b) What would a sampling distribution of sample size 10 look like? c) What would a sampling distribution of sample size 50 look like?

5. A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the mean of the combined random variable X+Y?