1. The data in the following table represent the number of miles per gallon achieved on the highway for compact cars for the model year 2005.
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1 Millersville University Name Department of Mathematics MATH 130, Elements of Statistics I, Test 2 March 5, 2010, 10:00AM-10:50AM Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of statistical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. The data in the following table represent the number of miles per gallon achieved on the highway for compact cars for the model year (a) (15 points) Find the five-number summary for these data.
2 (b) (5 points) Construct a box plot for the data
3 2. (3 points each) The following table represents the medal tallies of the top eight countries in the 2010 Winter Olympics in Vancouver. Country Gold Silver Bronze United States Germany Canada Norway Austria Russian Federation Korea China (a) If a medal is randomly selected from the top eight countries, what is the probability it is gold? (b) If a medal is randomly selected from the top eight countries, what is the probability it was won by Korea? (c) If a medal is randomly selected from the top eight countries, what is the probability it was gold and was won by Korea?
4 (d) If a medal is randomly selected from the top eight countries, what is the probability it was gold or was won by Korea? (e) If a bronze medal is randomly selected from the top eight countries, what is the probability it was won by Norway? (f) If a medal that was won by Norway is randomly selected, what is the probability that it is silver?
5 3. (4 points each) The following data represent (in thousands) the number of 5- to 9-yearold females in the United States in X (age) Freq. Rel. Freq (a) Verify that the relative frequency column is a probability distribution for the ages. (b) Find the mean of the random variable X. (c) Find the standard deviation of the random variable X.
6 4. (6 points) The Pennsylvania Mega Millions lottery requires a player to select (without repetition) five numbers from 1 to 56, and then one number (called the Mega Ball) from 1 to 46. The Mega Ball number picked can be the same as one of the first five numbers picked. In how many different ways can the Mega Millions lottery ticket numbers be selected? 5. (4 points each) According to the Higher Education Research Institute, 55% of college freshmen in 4-year colleges and universities are female. Suppose 15 freshmen are randomly selected and the number of females in the sample is observed. (a) Explain why the number of females in samples of 15 freshmen is a binomial random variable. (b) Find the probability that exactly 10 of the freshmen are female. (c) Find the probability that less than 8 of the freshmen are female.
7 (d) Find the probability that between 7 and 12 freshmen, inclusive, are female. 6. (4 points each) Before a criminal trial can begin, a jury of twelve impartial people must be selected. The pool of potential jurors, contains 20 men and 16 women. (a) How many different 12 member juries can be formed from this jury pool? (b) What is the probability of getting an all male jury of 12? (c) What is the probability of getting an all female jury of 12?
8 (d) What is the probability of getting a jury of 12 consisting of 6 men and 6 women? 7. (4 points) Lunesta is a drug for people with insomnia. One of the most common side effects of the drug is headache which occurs in 21% of people taking it. (a) If 150 users of Lunesta are randomly selected, what is the expected number of users who would experience headache as a side effect? (b) If 150 users of Lunesta are randomly selected, what is the standard deviation in the number of users who would experience headache as a side effect? (c) Would it be unusual to observe 45 reports of headache out of 150 users of Lunesta?
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