Spring 2015 Math227 Test #2 (Chapter 4 and Chapter 5) Name
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1 Spring 2015 Math227 Test #2 (Chapter 4 and Chapter 5) Name Show all work neatly and systematically for full credit. You may use a TI calculator. Total points: 100 Provide an appropriate response. 1) (5) A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz? 2) (5) A motel has a policy of booking as many as 150 guests in a building that holds 140. Past studies indicate that only 85% of booked guests show up for their room. Find the probability that if the motel books 150 guests, not enough seats will be available. 3) (6) The local police department receives an average of two calls per hour. (a). Find the probability that in a randomly selected hour the number of calls is three. (b). Find the probability that in a randomly selected hour the number of calls is at least one. 1
2 4) (15) According to government data, the probability that an adult was never in a museum is 15%. A random sample of 25 adults were surveyed. (a). What is the probability that two or fewer were never in a museum? (b). What is the probability that exactly three adults were never in a museum? (c). What is the probability that at least two adults were never in a museum? (d). Find the mean and standard deviation of the number of adults that were never in a museum. (e). Would it be unusual to have at 15 adults that were never in a museum? Explain. 2
3 5) (5) The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $4200 (1 chance in 8000); $1600 (1 chance in 6900); $500 (1 chance in 3300); $300 (1 chance in 2000). Find the expected value of the amount won for one entry if the cost of entering is 45 cents. (6) Solve the problem. 6) (a). How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed? (b). How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is allowed? (c). How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if the first digit must be 5, the last digit must be 1, and repetition is not allowed. 3
4 7) (5) A state lottery involves the random selection of six different numbers between 1 and 31. If you select one six number combination, what is the probability that it will be the winning combination? (18) Find the indicated probability. 8) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Men Women If one subject is randomly selected. (a). find the probability that the person chosen is a woman given that the person is a light smoker. (b). Find the probability that the person is a nonsomoker given that it is a woman. (c). Find the probability that the person chosen is a woman or a nonsmoker. (e). Find the probability that the person chosen is a nonsmoker and is a woman. If two subjects are randomly selected. (f). Find the probability that both of them are nonsmokers. (g). Find the probability that both of them are women. 4
5 Solve the problem. 9) (5) There are 6 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? Find the indicated probability. Round to the nearest thousandth. 10) (5) In a batch of 8,000 clock radios 2% are defective. A sample of 10 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected? Provide an appropriate response. Round to the nearest hundredth. 11) (5) The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate Office. Its probability distribution is as follows. Find the mean and the standard deviation for the probability distribution. Houses Sold (x) Probability P(x)
6 12) (6) A card is drawn from a well-shuffled deck of 52 cards. (a). Find the probability of drawing a face card or a 4. (b). Find the probability of drawing a queen given that it is a face card. (c). Find the probability of drawing a black queen. 13) (9) Dice. (a) A pair of dice are rolled 4 times, what is the probability of getting a sum of 7 every time? (b). A pair of dice are rolled once, what is the probability of getting a sum of 7 or sum of 11? (c). A pair of dice are rolled once, what is the probability of getting a sum of 8 given that it is a double? 14) (5) A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects. What is the probability that at least one of the calculators is defective? 6
C) 1 4. Find the indicated probability. 2) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?
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