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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Suppose a random variable is distributed as Student’s t distribution with (n - 1) degrees of freedom. Consider the probability P(t ≥ .7). Explain the relationship between the probability and the
The incomes of families in a town are assumed to be uniformly distributed between $15,000 and $85,000. What is the probability that a randomly selected family will have an income above $40,000?
At an antiques auction, the winning bids were found to be uniformly distributed between $500 and $2,500. What is the probability that a winning bid was less than $1,000? What is the probability that
The manager of a department store notices that the amount of time a customer must wait before being helped is distributed uniformly between 1 and 4 min.Find the mean and variance of the time a
A quality control expert for the Healthy Time Cereal Company notices that in a 16-oz package of cereal, the amount in the box is uniformly distributed between 15.3 and 17.1 oz. Find the mean and
The shelf life of hearing aid batteries is found to be approximated by an exponential distribution with a mean of 1/12 day. What fraction of the batteries would be expected to have a shelf life
A computer programmer has decided to use the exponential distribution to evaluate the reliability of a computer program. After 10 programming errors were found, the time (measured in days) to find
An advertising executive believes that the length of time a television viewer can recall a commercial is distributed exponentially with a mean of .25 days.Find how long it will take for 75 % of the
An investment advisor believes that the rate of return for Horizon Company’s stock is uniformly distributed between 3 % and 12 %. Find the probability that the return will be greater than 5 %. Find
The mean life of a computer’s hard disk is found to be exponentially distributed with a mean of 12,000 h. Find the proportion of hard disks that will have a life greater than 20,000 h.
Suppose the life of a car battery is assumed to be uniformly distributed between 3.9 and 7.3 years. Find the mean and variance of the life of a car battery.
The chief financial officer at Venture Corporation believes that an investment in a new project will have a cash flow in year one that is uniformly distributed between $1 million and $10 million.
The campus bus at Haverford College is scheduled to arrive at the business school at 8:00 a.m. Usually, the bus arrives at the bus stop during the interval 7:56–8:03. Assume that the arrival time
A gas station’s owner found that about two cars come into the station every minute. If the arrival time follows an exponential distribution, what is the probability that the next car will arrive in
A college professor gives a standardized test to her students every semester.She finds that the students’ grades follow a uniform distribution with 100 points as the maximum and 65 points as the
Briefly explain how the mean, standard deviation, coefficient of variation, and skewness can be used to analyze the returns of IBM and Boeing in Table 9.1.Table 9.1 Company name 1 3M Co. 2 Alcoa Inc.
Suppose the weight of a football team is uniformly distributed with a minimum weight of 175 lb and a maximum weight of 285 lb.(a) Find the mean weight of the team.(b) Compute the standard deviation
A bank manager finds that about six customers enter the bank every 5 min. If the customer arrival time follows an exponential distribution, what is the probability that the next customer will arrive
Suppose the life of a steel-belted radial tire is uniformly distributed between 30,000 and 45,000 miles.(a) Find the mean tire life.(b) Find the standard deviation of tire life.(c) What percentage of
Briefly discuss the relationship among and F distributions. 2 t, X
Given v1 = 5 and a = .05, find v2 for the following F values.(a) 5.05(b) 3.33(c) 2.53
In their study, Vardeman and Ray found that the number of accidents per hour at an industrial plant is exponentially distributed with a mean λ = .5. Use the formula f(t) = λe - λt to determine
Suppose there is a sample of 30 items drawn from a normal population. Find the probability that the sample variance exceeds 36.6869.
Suppose there are two independent normal populations with population variances o = 4.5 and o2 = 2.5, respectively. Two random samples of sizes s and s2, respectively, are drawn from the two normal
A random sample of size 7 is drawn from a population with population variance σ2 = 2.5.(a) Determine the probability that the variance of the sample is greater than 7.008.(b) Determine the
The following random sample is taken from a normal population.(a) If the population man is μ = 60, what is t statistics for the sample?(b) If the population man is μ = 55, what is t statistics for
For the following results from samples drawn from normal populations, what are the best estimates for the mean, the variance, the standard deviation, and the standard deviation of the mean? (a) n =
For each of the following samples drawn from normal populations, find the best estimates for μ, σ1, σ, and the standard deviation of X̅.(a) 4, 10, 2, 8, 4, 14, 12, 8, 30(b) –4, 2, –6, 0, 6,
Find the value of zα|2 for the following values of a. .01 b. c. a = .002 = (a) a (b) = .03 (c) a = .002
A stockbroker has taken a random sample of 4 stocks from a large population of low-priced stocks. Stock prices for this population are normally distributed.The sample prices of the 4 stocks are $5,
A 90%confidence interval for the population mean time (in minutes) needed to finish a certain assembly process is 90 < μx < 130.(a) Sketch this interval, indicating the margin for sampling error.(b)
Assuming you have samples from normal populations with known variance, find(a) The degree of confidence used if n = 19, σ = 8, and the total width of a confidence interval for the mean is 3.29
(a) Find the value of t such that the probability of a larger value is .005 when the value for the degrees of freedom is very large.(b) Find the value of t such that the probability of a smaller
A poll reported that 48 % of probable voters seem determined to vote against the president. Assume that this sample was based on a random selection of 789 probable voters. Construct a 99 % confidence
A survey of low-income families in New Jersey was designed to determine the average heating costs for a family of 4 during January and February. Heating costs are known to have a standard deviation
A company has just installed a new automatic milling machine. The time it takes the machine to mill a particular part is recorded for a sample of 9 observations. The mean time is found to be X̅ =
A survey indicated that companies with fewer than 1,000 employees are expected to increase their spending by 20.4 %. Form a 99 % confidence interval for the unknown mean increase, assuming that the
A study conducted in 1984 reported that the median pay in the United States was $18,700. What difficulties do you see in using this type of study for assessing incomes? Would you be willing to use
What is an unbiased estimator? What is an efficient estimator? What is a consistent estimator? Why are these concepts important?
Briefly explain why we sometimes construct confidence intervals for the population mean.
Explain what happens to the size of the confidence interval when(a) The standard deviation increases.(b) The standard deviation decreases.(c) The probability content (1 - α) increases from 95 % to
Labor economists at the Department of Labor say they have 95 % confidence that factory workers’ earnings will lie between $22,000 and $61,000. Explain what this means.
Reconstruct the confidence interval for the mean home prices given in question 18, but this time construct a 99 % confidence interval. What happens to the size of the confidence interval?Question 18A
Again, use the information given in question 18. This time assume that 100 homes are randomly sampled instead ofQuestion 18A real estate agent in Connecticut is interested in the mean home price in
Construct a 95 % confidence interval for the mean home price. What happens to the size of the confidence interval?
Again, use the information given in question 18. This time, assume that the sample standard deviation is $28,000. Construct a 95 % confidence interval for the mean home price. What happens to the
A random sample of 200 students at Academic University finds the sample mean grade point average to be 3.10 with a standard deviation of 0.80.Construct a 99 % confidence interval for the mean grade
An insurance company is interested in the average claim on its auto insurance policies. It believes the claims are normally distributed. Using the last 37 claims, it finds the mean claim to be $1,270
A random sample of the luggage of 30 passengers of Fly Me Airlines finds that the mean weight of the luggage is 47 lb with a standard deviation of 8 lb.Construct a 90 % confidence interval for the
A bank manager finds from reviewing her records that the amount of money deposited on Saturday morning is normally distributed with a standard deviation of $150. A random sample of 7 customers
Redo question 27, parts (a) and (b), this time assuming the population standard deviation is unknown. Use MINITAB.Question 27A bank manager finds from reviewing her records that the amount of money
A quality control engineer believes that the life of light bulbs for his company is normally distributed with a standard deviation of 100 h. A random sample of 10 light bulbs gives the following
A credit manager at the Bargain Basement Department Store is interested in the proportion of customers who pay their credit card balances in full each month.A random sample of 200 customers indicates
Managers at the Smooth Ride Car Rental Company are interested in the mean number of miles that people drive per day. From past experience, they know that the standard deviation is 75 miles. A random
Construct point estimates for the following situations:(a) A labor union randomly samples 75 of its members and finds that 40 favor the new contract. Estimate the proportion of all workers who favor
Reviewing his records, a grocery store manager finds that the amount of money spent shopping on Friday evenings is normally distributed with a standard deviation of $22. A random sample of 5
A random sample of 75 observations from a population yielded the following summary statistics:Construct a 95 % confidence interval for the population mean m. x=1,270 x = 21,520
A random sample of 100 observations from a population yielded the following summary statistics:Construct a 99 % confidence interval for the population mean μ. = 375 (x x) = 972 2 -
Suppose a random sample of 40 professional golfers is taken and the mean scoring average of the sample is found to be 72.8 strokes per round with a standard deviation of 1.2 strokes per round.
Suppose a random sample of 10 professional golfers is taken and the mean scoring average of the sample is found to be 71.8 strokes per round with a standard deviation of 1.3 strokes per round.
Reconsider the information given in question 40. Suppose now that the population standard deviation is known to be 1.3 strokes per round. Construct a 90%confidence interval for the population mean
Suppose you construct a 95 % confidence interval for the mean of an infinite population. Will the interval always be narrower when σ is known than when σis unknown?
In a national survey, 200 cola drinkers were asked to compare Yum Yum Cola to Yuk Yuk Cola. Of the 200 people sampled, 120 preferred Yum Yum.Construct a 95 % confidence interval for the actual
The 80 members of a random sample of graduates of Mary’s Typing School indicate that their mean salary is $22,500 with a sample standard deviation of $3,100. Construct a 99 % confidence interval
Suppose a random sample of 30 college students reveals that the mean amount of money spent on textbooks each semester is $ 145 with a standard deviation of $25. Construct a 90 % confidence interval
The Better Health Cereal Company produces Healthy Oats cereal. A sample of 100 boxes of this cereal indicates that the mean weight of a box of cereal is 24 oz with a standard deviation of 1 oz.
The Better Health Cereal Company produces Healthy Oats cereal. A sample of 15 boxes of this cereal indicates that the mean weight of a box of cereal is 24 oz with a standard deviation of 1 oz.
A sample of 100 former basketball players from Slam Dunk University shows that 55 of the players graduated in 4 years. Construct a 90 % confidence interval for the proportion of basketball players
A sample of 20 cups of coffee from a coffee machine has a mean amount of coffee of 6 oz. The standard deviation is known to be .5 oz. Construct a 99 %confidence interval for the mean amount of coffee
Reconsider question 50. This time, assume that the standard deviation is not known and that .5 oz is the sample standard deviation. Again construct a 99 %confidence interval for the mean amount of
Suppose a sample of 500 companies listed on the NYSE is found to contain 327 companies paying dividends that have increased over the last year. Construct a 95 % confidence interval for the mean
A sample of 100 steel-belted radial tires yields a mean life of 35,000 miles with a sample standard deviation of 4,000 miles. Construct a 90 % confidence interval for the mean life of steel-belted
Suppose a bowler takes a random sample of 15 games she has bowled and finds the sample mean to be 172. She knows that the standard deviation of her score is 8. Construct a 99 % confidence interval
Flip a coin 50 times and record the number of tails. Construct a 99 % confidence interval for the proportion of tails in the tossing of a coin.
A random sample of 450 people who took Dollar Dave’s CPA review course reveals that 310 of them passed the CPA exam on the first try. Construct a 90 %confidence interval for the proportion of
A random sample of 200 observations from a population yielded the following summary statistics:Construct a 90 % confidence interval for the population mean μ.. x=1,202 x2 = 121,020
A random sample of 225 people who went to the Matchmaker Dating Service finds that 100 of those people found their spouse through the service. Construct a 95 % confidence interval for the proportion
A random sample of 80 observations from a population yielded the following summary statistics:Construct a 95 % confidence interval for the population mean μ. x=475 ( x) = 772
A random sample of 100 bullets in a case of 1,000 includes 5 that are defective. Construct a 99 % confidence interval for the proportion of defective bullets in a case.
Suppose a golfer on the University of Houston golf team plays 70 rounds of golf and breaks par 32 times. Construct a 90 % confidence interval for the proportion of rounds in which this golfer will
You roll a die 100 times and get the following results.Construct a 90 % confidence interval for the proportion of rolls that will be 1 s. Number on die 1 2 3 4 5 16 Number of rolls 13 16 15 14 22 20
Use the information given in question 62 to construct a 90 % confidence interval for the proportion of rolls that will come up 6.Question 62Suppose a golfer on the University of Houston golf team
A surge in health insurance premiums imposes an additional burden on a business. A random sample of 10 employees indicates that the average cost increase per employee is about $2,345 with a standard
The owner of a local bakery feels that too many bagels are thrown out every night, so he decides to estimate the demand for bagels. After a month’s observation, he collected 30 days’ sales and
Suppose the owner in question 65 observed the sales for 60 days and found the average sales to be 115 with a standard deviation of 12. Obtain the 90 % confidence interval for the demand for
The manager in the local shoe factory wants to estimate the productivity of the midnight shift. He draws a random sample of 10 nights and records the productivity as follows:(a) Estimate the average
A local dairy farm has just installed a new machine that pumps milk into 16-oz bottles. The manager of the farm wants to make sure that the amount of milk put in the bottles is 16 oz, so he randomly
The personnel office found that in the last 5 years, the average cost of recruiting management trainees has been $500. The cost varies but follows a normal distribution. The standard deviation is
A survey wherein 90 employees were randomly drawn shows that the average number of sick days taken by employees each year is 5.4 days. The number of sick days follows a normal distribution with a
A recent poll shows that 53 % of the voters interviewed strongly support the incumbent and are willing to vote for her in the coming election. The poll was taken by asking 1,000 voters. Estimate the
A consumer rights organization tests a new car to estimate the car’s average gasoline mileage. Because its budget is limited, the organization can test only 25 cars. The standard deviation of the
A poll is conducted to predict whether new municipal bonds should be issued.Assume that 230 out of 500 interviewees voted for issuance of the new bonds.How precise is this prediction? Construct a 95
In question 73, assume that 45 % of the entire population of voters support issuance of the new bonds. Under this condition, if the pollsters want to stay within 2%error (plus and minus 1 %), how
A multinational company wants to find out how society perceives it. The company sends a questionnaire to 2,000 people and learns that 893 have favorable opinions and others either have an unfavorable
When we construct a 90 % confidence interval for, say, a mean, we build a range that has an upper bound and a lower bound, and we write the confidence interval as P(lower bound < mean < upper bound)
A new machine was designed to cut a metal part at a length of .24 in.. Although the machine is well designed, for some uncontrolled reasons, the machine cuts the metal with a standard deviation of
The trains scheduled to arrive at the New Brunswick train station at 7:35 A.M. every weekday do not always arrive at 7:35. A commuter carefully recorded the arrival time for the last 200 working days
A marketing consulting company wants to estimate the percentage of students holding credit cards by sending questionnaires to students. The sponsor of this research wants to establish a 95 %
In a survey of 2,000 voters, 36%were found to support increasing taxes to build a new school system. Obtain the 95 % confidence interval for the proportion supporting the tax increase.
The manager in the local supermarket wanted to know whether it is worth the trouble to keep the store open 24 h a day. He randomly sampled and recorded 20 nights’ sales and gotUse M1NITAB to answer

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