Problem : 1

A serious disease called senioritis is often caught by certain groups of young people. Suppose 25% of the college-aged population has senioritis. A test is used to detect senioritis in this population, but is not always accurate. The test gives a correct positive (sensitivity) result 90% of the time. The test also gives a correct negative result (specificity) 85% of the time. (Hint: Draw a tree diagram). Use this information to find the following:

1. Find the probability that a randomly selected college-aged student has senioritis and tested positive.
2. Find the probability that a student selected randomly has a senioritis given a positive test result.
3. Find the conditional probability that a person has senioritis given a negative test result.
4. Find the probability that a student selected randomly does not have a senioritis given a negative test result.

Problem 2: A soccer team estimates that they will score on 8% of the corner kicks. In next week's game, the team hopes to kick 15 corners kicks. Define X: # of scores the team is making from the kicks.

1. What an appropriate model for the random variable
2. What are the chance that they will score on 2 of those opportunities?
3. Determine the probability that the team miss 5 kicks.

Problem 3: An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.

1. Describe parameter of interest for this study. Determine the point estimation of the parameter.
2. Find the mean and standard deviation for the sampling distribution model for. What do mean and standard error measure?
3. Write an appropriate probability model for sample proportion.