• Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from program software packages will not be accepted.
1. Assume that you toss a fair coin 5 times.
(a) What is the probability that you get 5 heads? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting heads in the 5th toss, given that the first four tosses are tails? (Show work and write the answer in simplest fraction form)
(c) If event A is "Getting heads in the 5th toss" and event B is "The first four tosses are tails". Are event A and event B independent? Please explain.
2. A high school with 1000 students offers two foreign language courses : French and Japanese. There are 150 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. (Show work and write the answer in simplest fraction form)
3. Imagine you are in a game show. There are 5 prizes hidden on a game board with 20 spaces. One prize is worth $500, another is worth $200, and three are worth $50. You have to pay $50 to the host if your choice is not correct. Let the random variable x be the winning.
• Complete the following probability distribution. (Show the probability in fraction format and explain your work)
• What is your expected winning in this game? (Show work and round the answer to two decimal places)
• What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)
4. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. If her opponent serves 10 times, answer the following questions:
(a) What is the probability that she returns at least 2 of the 10 serves from her opponent? (Show work and round the answer to 4 decimal places)
(b) How many serves can she expect to return? (Hint : What is the expected value?) (Show work and round the answer to 2 decimal places)
5. If the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the probability that a randomly selected person has an IQ score between 88 and 118. (Show work and round the answer to 4 decimal places)
(b) If 100 people are randomly selected, what is the standard deviation of the sample mean IQ score. (Show work and round the answer to 2 decimal places)
(c) If 100 people are randomly selected, find the probability that sample mean IQ score is greater than 97. (Show work and round the answer to 4 decimal places)
6. Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi is designing a plane with a height that allows 95% of the men to stand straight without bending in the plane. What is the minimum height of the plane? (Show work and round the answer to 2 decimal places)
7. There are 10 members in the UMUC Stats Club.
(a) The Club must select a president, a vice president and a treasurer for the school year. How many different ways can the officers be selected? (Show work)
(b) The Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. How many different ways can the delegate be selected? (Show work)