# Mathematics

1.) Two thousand frequent business travelers are asked which midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. 107 liked Indianapolis best, 454 liked Saint Louis, 1370 liked Chicago, and the remainder preferred Milwaukee. Develop a frequency table and a relative frequency table to summarize this information. (Round relative frequency to 3 decimal places.) City Frequency Relative Frequency Indianapolis St. Louis Chicago Milwaukee 2.) In June an investor purchased 350 shares of Oracle (an information technology company) stock at $22 per share. In August she purchased an additional 420 shares at $25 per share. In November she purchased an additional 510 shares at $31 per share. What is the weighted mean price per share? (Round your answer to 2 decimal places. Omit the “$” sign in your response.) The weighted mean is $ 3. Sally Reynolds sells real estate along the coastal area of Northern California. Below is the total amount of her commissions earned since 2000. Year Amount (thousands) 2000 $237.51 2001 233.8 2002 206.97 2003 248.14 2004 164.69 2005 292.16 2006 269.11 2007 225.57 2008 255.33 2009 202.67 2010 206.53 Find the mean, median, and mode of the commissions she earned for the 11 years. (Round your answers to 2 decimal places.) Mean Median Mode 4.The unemployment rate in the state of Alaska by month is given in the table below: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 7.00 7.20 6.60 8.80 7.40 7.60 7.50 8.30 7.10 7.20 7.80 8.60 (a) What is the arithmetic mean of the Alaska unemployment rates? (Round your answer to 2 decimal places.) Arithmetic mean (b) Find the median and the mode for the unemployment rates. (Round your answers to 2 decimal places.) Median Mode 5.) A sample of the personnel files of eight employees at the Pawnee location of Acme Carpet Cleaners, Inc., revealed that during the last six-month period they lost the following number of days due to illness: 5 5 4 4 1 2 0 6 A sample of eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost the following number of days due to illness. 2 1 0 10 2 2 3 0 (a) Calculate the range, mean and mean deviations for the Pawnee location and the Chickpee location.(Round mean and mean deviation to 2 decimal places.) Pawnee location Chickpee location Range Mean Mean deviation (b-1) Based on the sample data, which location has fewer lost days? (b-2) Based on the sample data, which location has less variation? 6. The annual report of Dennis Industries cited these primary earnings per common share for the past 5 years: $2.29, $1.18, $2.22, $4.42, and $3.4. (a) What is the arithmetic mean primary earnings per share of common stock? (Round your answer to 2 decimal places.) Arithmetic mean (b) What is the variance? (Round your answer to 2 decimal places.) Variance The distribution of the weights of a sample of 1,500 cargo containers is symmetric and bellshaped. (a) According to the Empirical Rule, what percent of the weights will lie between and ?(Omit the “%” sign in your response.) Percent of the weights % (b) According to the Empirical Rule, what percent of the weights will lie between and ? (Round your answer to 2 decimal places. Omit the “%” sign in your response.) Percent of the weights % (c) Below ? (Round your answer to 2 decimal places. Omit the “%” sign in your response.) Percent of the weights % 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 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 31. A normal population has a mean of 22 and a standard deviation of 5. (a) Compute the z value associated with 25 (Round your answer to 2 decimal places.) Z (b) What proportion of the population is between 22 and 25? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion (c) What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion