# MATHEMATICS

15. The credit department of Lion’s Department Store in Anaheim, California, reported that 28 percent of their sales are cash or check, 30 percent are paid with a credit card and 42 percent with a debit card. Twenty percent of the cash or check purchases, 85 percent of the credit card purchases, and 70 percent of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash or check? (Round your answer to 3 decimal places.) Probability 16. Solve the following: (a) (b) 9P5 = (c) 9C6 = 17. An overnight express company must include seven cities on its route. How many different routes are possible, assuming that it matters in which order the cities are included in the routing? Number of different routes 18.) The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,080 0.6 1,440 0.1 1,640 0.3 (1) What is the expected number of admissions for the fall semester? Expected number of admissions (2) Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.) Variance Standard deviation 19. The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 15 $ 3 2 35 6 3 47 11 4 40 16 5 35 22 6 17 25 7 6 27 8 33 29 228 (a) Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8 (b-1) Find the mean and the standard deviation of the number of hours parked. (Round your intermediate values and final answers to 3 decimal places.) Mean Standard deviation (b-2) How long is a typical customer parked? (Round your answer to 3 decimal places.) The typical customer is parked for hours (c) Find the mean and the standard deviation of the amount charged. (Round your intermediate values and final answers to 3 decimal places.) Mean Standard deviation 20. In a binomial situation, n = 7 and .20. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.) (a) x = 5 Probability (b) x = 6 Probability 21. Industry standards suggest that 8 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 10 Nissans yesterday. (Round your Mean answer to 2 decimal places and the other answers to 4 decimal places.) (a) What is the probability that none of these vehicles requires warranty service? Probability (b) What is the probability exactly one of these vehicles requires warranty service? Probability (c) Determine the probability that exactly two of these vehicles require warranty service. Probability (d) Compute the mean and standard deviation of this probability distribution. Mean µ Standard deviation σ 22. In a binomial distribution, and . Find the probabilities of the following events. (Round your answers to 4 decimal places.) (a) Probability (b) Probability (c) Probability 23. Keith’s Florists has 16 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 16 trucks, 8 have brake problems. A sample of 5 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes? (Round your answer to 4 decimal places.) Probability 24. The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 7 of the 36 possible numbers. Assume there are 36 ping-pong balls each with a single number between 1 and 36. Any number appears only once, and the winning balls are selected without replacement. (a) The commission reports that the probability of matching all the numbers are 1 in 8,347,680. What is this in terms of probability? (Round your answer to 8 decimal places.) Probability (b) Use the hypergeometric formula to find this probability. The lottery commission also pays if a contestant matches 5 or 6 of the 7 winning numbers. Hint: Divide the 36 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.) Probability (c) Find the probability, again using the hypergeometric formula, for matching 5 of the 7 winning numbers.(Round your answer to 8 decimal places.) Probability (d) Find the probability of matching 6 of the 7 winning numbers. (Round your answer to 8 decimal places.) Probability 25. n a Poisson distribution, . (Round your answers to 4 decimal places.) (a) What is the probability that ? Probability (b) What is the probability that ? Probability 26. It is estimated that .48 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. What is the probability that of today’s 1,400 callers at least 5 received a busy signal? Use the poisson approximation to the binomial. (Round your answer to 4 decimal places.) Probability 27. Assume a binomial probability distribution with and . Compute the following: (Round all zvalues to 2 decimal places.) (a) The mean and standard deviation of the random variable. (Round your “σ” to 4 decimal places and mean to 1 decimal place.) μ σ (b) The probability that X is 20 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability (c) The probability that X is 16 or less. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability 28. For the most recent year available, the mean annual cost to attend a private university in the United States was $20,332. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,250. Ninety-nine percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number. Omit the “$” sign in your response.) Amount $ 29. Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,050 per hour and a standard deviation of $195. What is the operating cost for the lowest 4 percent of the airplanes? (Round z value to 2 decimal places. Omit the “$” sign in your response.) Operating cost $ 30. The number of viewers of American Idol has a mean of 32 million with a standard deviation of 4 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will: (a) Have between 36 and 43 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (b) Have at least 29 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (c) Exceed 47 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability