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.
Survey Results
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 value couldn’t possibly be 3.5. Who is right? Use a table to help explain your response.
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 distributed.
