# MATHEMATICS

7.) The IRS was interested in the number of individual tax forms prepared by small accounting firms. The IRS randomly sampled 51 public accounting firms with 10 or fewer employees in the DallasFort Worth area. The following frequency table reports the results of the study. (Round your answers to 2 decimal places.) Number of Clients Frequency 15 up to 30 2 30 up to 45 13 45 up to 60 23 60 up to 75 8 75 up to 90 5 Mean Standard deviation 8. The following stem-and-leaf chart from the MINITAB software shows the number of units produced per day in a factory. 1 3 7 1 4 2 5 6 9 6 0133589 7 7 0236788 9 8 56 7 9 00156 2 10 38 (Leave no cells blank, be certain to zero whenever required.) (a) How many days were studied? (b) How many observations are in the first class? (c) What are the minimum value and maximum values? The minimum is , the largest is (d) List the actual values corresponding to the last two entries in the fourth row. (e) How many values are there in the second row? (f) How many values are less than 70? (g) How many values are 80 or more? (i) How many values are between 60 and 89, inclusive? 9. The Thomas Supply Company, Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company, Inc. invoices. 13 13 13 20 26 28 30 33 34 34 35 35 36 37 38 41 41 41 45 46 47 47 49 52 53 55 56 62 67 82 (Round your answers to 2 decimal places.) (a) Determine the first and third quartiles. Q1 = Q3 = (b) Determine the second decile and the eighth decile. D2 = D8 = (c) Determine the 67th percentile. 10. Listed below are the commissions earned ($000) last year by the sales representatives at the Furniture Patch, Inc. Assume that this is sample data (i.e., calculate a sample standard deviation). 3.9 6.1 7.5 11.2 12.9 13.6 15.3 15.8 16.9 17.4 18.3 22.3 36.5 43.2 82.9 (a) Determine the mean, median, and the standard deviation. (Round your answers to 2 decimal places.) Mean Median Standard deviation (b) Determine the coefficient of skewness using Pearson’s method. (Round your answer to 3 decimal places.) Coefficient of skewness (c) Determine the coefficient of skewness using the software method. (Round your answer to 2 decimal places.) Coefficient of skewness 11. The events and are mutually exclusive. Suppose and (a) What is the probability of either or occuring? (Round your answer to 2 decimal places.) Probability of either or (b) What is the probability that neither nor will happen? (Round your answer to 2 decimal places.) Probability of neither nor 12. A study of 203 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under $1 million 106 $1 million to $20 million 51 $20 million or more 46 (a) What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.) Probability (b-1) What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.) Probability (b-2) What rule of probability could be applied? Rule of Probability 13. A student is taking two courses, history and math. The probability the student will pass the history course is .59, and the probability of passing the math course is .74. The probability of passing both is .41. What is the probability of passing at least one? (Round your answer to 2 decimal places.) Probability 14. All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .79, the probability the second truck is available is .60, and the probability that both trucks are available is .43: What is the probability neither truck is available? (Round your answer to 2 decimal places.) Probability 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