In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether this is a probability distribution. Give two reasons why you believe it is a probability distribution or give two reasons why you believe it does not satisfy the probability distribution requirements. Contributes Most to Happiness P(x) Family 0.77 Friends 0.15 Work/Study 0.08 Leisure 0.08 Music 0.06 Sports 0.04.

In a recent U.S. Open tennis tournament, among 20 of the calls challenged by the players, 8 were overturned after a review using an electronic system. Assume that when players challenge calls, they are successful in having them overturned 50% of the time. What is the probability that among 20 challenges, 8 or fewer are overturned? Does this result suggest that the success rate is less than 50%? Why or why not?

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected.

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distrib