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# Intermed Bus Stat MAS 202

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This 8 page Class Notes was uploaded by Mr. Theodore Herzog on Thursday September 17, 2015. The Class Notes belongs to MAS 202 at University of Miami taught by Staff in Fall. Since its upload, it has received 184 views. For similar materials see /class/205761/mas-202-university-of-miami in Management Science (Mas) at University of Miami.

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Date Created: 09/17/15

1b MAS 202 REVIEW EXERCISES t V According to the US Bureau of Labor Statistics 5 of people working in the United States moonlight ie they hold a secondjob Using the binomial probabilities table nd the probability that the number of workers who moonlight in a random sample pf H workers is V i 15 a at most 5 b at least 1 c 3to6 The Food and Drug Administration approves 20 of drugs submitted for its appr val U 8 News amp World Report January 23 P1989 Using the binomial probabilities table nd the probability that in a random sample of 15 drugs submitted forthe FDA s approval the number of drugs that are approved is a less than 4 b more than 6 c 2 to 5 x 2a 2b A large proportionof small businesses in the United States fail during the rst few years of operation On average 13 businesses le for bankruptcy per day in a large city a Find the probability that 3 businesses will le for bankruptcy on a given day in this city Find the probability that the number of businesses that will le for bankruptcy on a given day in this city is i 2 to 3 ii morefthan 3 iii less than 3 The reception of ce at Tom s Building Corporation receives an average of 49 phone calls per half hour a Find the probability that exactly 6 phone calls will be received at this of ce during a certain hour Find the probability that the number of phone calls received at this of ce during a certain hour will be I i less than 8 ii more than 12 i 3a 3b The Bank of Connecticut issues Visa and Mastercard credit cards It is estimated that the balances on all Visa credit Cards issued by the Bank of Connecticut have a mean of 845 and a standard deviation of 270 Assume that the balances on all these Visa cards follow arnormal distribution t r a What is the probability that a randomly selected Visa card issued by this bank has a balance between 1000 and 1400 i b What percentage of the Visa cards issued by this bank have a balance of 750 or more A health insurance company pays its members a maximum of 500 per year for prescription drugs If a member spends more than 500 on prescription drugs during a year any amount over 500 is paid either by the member or by the major medical insurance 1The past data39show that the annual expenses on prescription drugs for all members of this company have a normal distribution with a mean of 350 and a standard deviation of 65 a 1 What percentage of the members Of this health insurance company exceed the maximum annual expenses allowed by the company on prescription drugs I l b What percentage of the members of this health insurance company spend less than 200 per year on prescription drugs 1 I 4 i 4a 4b 5a The amounts of electric bills for all households in a city have a skewed probability distribution with a mean of 65 and a standard deviation of 25 Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be A more than 70 b between 58 and 63 c within 6 of the population mean J c more than the population mean by at least 5 1 A machine at Katz Steel Corporation makes 3inchlong nails The probability distribution of the lengths of these nails is normal with a mean of 3 inches and a standard deviation of 1 inches The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these nails If the mean of this sample is eitheri less than 295 inches or greater than 305 inches the inSpector concludes that the machine needs an adjustment What is the probability that based on a sample of 25 nails the inspector will conclude that the machine needs an adjustment F The high cost of health care is a matter of major concern for a large number of families A random sample of 25 families selected from an area showed that they spend an average of 120 per month on health care with a standard deviation of 28 Make a 99 con dence interval for the mean health care expenditure per month incurred by all families in this ar a Assume that the monthly health care expenditures of all families in this area have a normal distribution 5b 6a 6b A company wants to estimate the mean net weight of its Top Taste cereal boxes A sample of 16 such boxes produced the mean net weight of 3 1 98 ounces with a standard deviation of 26ounces Make a 95 con dence interval for the mean net weight of all Top Taste cereal boxes Assume that the net weightsof all such cereal boxes have a normal distribution 4 4 39 l t According to a 1992 survey conducted by the Roper Organization for Shearson Lehman Brothers 45 of the persons polled said that they would change careers if they could The Wall Street Journal September 11992 Suppose this percentage is true for the 1992 population of all workers A researcher wanted to check whether this percentage is still true A sample of 350 workers taken recently by this researcher showed that approximately 39 of them would change careers if they could Using the 25 signi cance level can you conclude that the current percentage of workers who would change careers if they could is less than 45 2 According to the National Education Association 12 of school teachers have a second job to supplement their incomes USA TODAY July 7 1992 A random sample of 400 teachers taken this year showed that 19 of them hold a second job Testing at the 1 signi cance level can you conclude that the current percentage of all teachers who hold a second job to supplement their incomes is higher than 12 Explain your conclusion 7a 7b The management of a supermarket wanted to investigate if the male customers spend less money on average than the female customers A sample of 25 male customers who shopped at this supermarket showed that they spent an average of 73 with a standard deviation of 1750Another sample of 20 female customers who shopped at the same supermarket showed that they spent an average of 87 with a standard deviation of 1440 Assuine that the amounts spent at this supermarket by all male and all female customers are normally distributed with equal but unknown population standard deviations a Test at the 5 signi cance level if the mean amount spent by all male customers at this supermarket is less than that of all female customers An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 68 miles per hour with a standard deviation of 22 miles Another sample of 18 cars driven by 7 women on the same highway gave a mean speed of 65 miles per hour with a standard deviation of 25 miles Assume that the speeds at which all men and all Women drive cars on this highway are both normally distributed with the same population standard deviation a Test at the 1 signi cance level if the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers L 8a 8b According to the Bureau of LabofStatistics the mean hourly wage in February 1993 was 1362 for transportation and public utility workers and 1161 for manufacturing workers Assume that these two estimates are based on random samples of 1000 and 1200 workers taken respectively from the two populations Further assume that the stande deviations of the two populations are 185 and r 140 respectively a Test at the 5 signi cance level if the mean hourly wage for transportation and public utility workers in February 1993 was higher than that of manufacttning workers Professor Paul W Kingston and Steven L Nock studied the time spent together by singleand dualearner couples According to the records kept by wives in this study the mean time spent together by a husband and wife watching television was 616 minutes per day for singleeamer couples and 444 minutes per day for dualearner couples The respective sample sizes were 144 and 177 and the sample standard deviations were 790 and 568 minutes respectively Paul William Kingston and Steven L Nock Time Together Among Dualeamer Couples American Sociological Review 523 June 1987 pp 391400 a Test at the 1 signi cance level if the mean time spent together watching television by singleearner couples is higher than that of dualearner couples 7 I 39 V 9a 9b According to the US Bureau of the Census 488 of households headedby single women and 415 of households headed by single men own homes Assume that these estimates are based on random samples of 1640 households headed by single women and 1800 households headed by single men rw a Test at the 5 signi cance level if the proportion of households headed by single women who own homes is higher than the proportion of households headed by single men who own homes r I I The management of a supermarket wanted to investigate if the percentages of men 39 and women who prefer to buy national brand products over the store brand products are different A sample of 600 men shoppers at the company s supermarkets showed that 246 of them prefer to buy national brand products over the store brand products Another sample of 700 women shoppers at the company s supermarkets showed that 266 of them prefer to buy national brand products over the store brand products a Construct a 95 confidence interval for the di erence between the proportions of all men and all women shoppers at these supermarkets who prefer to buy national brand products over the store brand products

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