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Introductory Statistics 8th Edition Prem S. Mann - Solutions

The following table gives the probability distribution of the number of camcorders sold on a given day at an electronics store.Calculate the mean and standard deviation for this probability distribution. Give a brief interpretation of the value of the mean.
The following table, reproduced from Exercise 5.12, lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at Millard Fell more Memorial Hospital.Calculate the mean and standard deviation for this probability distribution.
Let x be the number of heads obtained in two tosses of a coin. The following table lists the probability distribution of x.Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
Indicate which of the following random variables are discrete and which are continuous. a. The amount of rainfall in a city during a specific month b. The number of students on a waitlist to register for a class c. The price of one ounce of gold at the close of trading on a given day d. The number
Let x be the number of potential weapons detected by a metal detector at an airport on a given day. The following table lists the probability distribution of x.Calculate the mean and standard deviation for this probability distribution and give a brief interpretation of the value of the mean.
Refer to Exercise 5.14. Calculate the mean and standard deviation for the probability distribution you developed for the number of defective tires on all 1300 H2 Hummer limousines. Give a brief interpretation of the values of the mean and standard deviation.In Exercise 14
Refer to Exercise 5.15. Find the mean and standard deviation of the probability distribution you developed for the number of remote starting systems installed per day by Al€™s Auto Security Shop over the past 80 days. Give a brief interpretation of the values of the mean and standard
Refer to the probability distribution you developed in Exercise 5.16 for the number of lemons in two selected cars. Calculate the mean and standard deviation of x for that probability distribution.
Refer to the probability distribution you developed in Exercise 5.17 for the number of uninsured motorists in a sample of two motorists. Calculate the mean and standard deviation of x for that probability distribution.
A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are $10 million from
An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 1000 tickets contain a prize of $5 each, 100 tickets have a prize of $10 each, 5 tickets have a prize of $1000 each, and 1 ticket has a prize of $5000. Let x be the random variable that denotes the net
Refer to the probability distribution you developed in Exercise 5.20 for the number of lefthanded persons in a sample of two persons. Calculate the mean and standard deviation of x for that distribution.
Refer to the probability distribution you developed in Exercise 5.21 for the number of athletes in a random sample of two who have used illegal performance-enhancing drugs. Calculate the mean and standard deviation of x for that distribution.
Briefly explain the following.a. A binomial experimentb. A trialc. A binomial random variable
What are the parameters of the binomial probability distribution, and what do they mean?
Which of the following are binomial experiments? Explain why. a. Rolling a die many times and observing the number of spots b. Rolling a die many times and observing whether the number obtained is even or odd c. Selecting a few voters from a very large population of voters and observing whether or
Which of the following are binomial experiments? Explain why. a. Drawing 3 balls with replacement from a box that contains 10 balls, 6 of which are red and 4 are blue, and observing the colors of the drawn balls b. Drawing 3 balls without replacement from a box that contains 10 balls, 6 of which
Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.a. P(x = 5) for n = 8 and p = .70b. P(x = 3) for n = 4 and p = .40c. P(x = 2) for n = 6 and p = .30Verify your answers by using Table I of Appendix C.
Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities. a. P(x = 0) for n = 5 and p = .05 b. P(x = 4) for n = 7 and p = .90 c. P(x = 7) for n = 10 and p = .60 Verify your answers by using Table I of Appendix C.
Let x be a discrete random variable that possesses a binomial distribution.a. Using Table I of Appendix C, write the probability distribution of x for n = 7 and p = .30 and graph it.b. What are the mean and standard deviation of the probability distribution developed in part a?
Let x be a discrete random variable that possesses a binomial distribution.a. Using Table I of Appendix C, write the probability distribution of x for n = 5 and p = .80 and graph it.b. What are the mean and standard deviation of the probability distribution developed in part a?
The binomial probability distribution is symmetric for p = .50, skewed to the right for p < .50, and skewed to the left for p > .50. Illustrate each of these three cases by writing a probability distribution table and drawing a graph. Choose any values of n (equal to 4 or higher) and p and
The most recent data from the Department of Education show that 34.8% of students who submitted otherwise valid applications for a Title IV Pell Grant in 2005–2006 were ineligible to receive such a grant (www2.ed.gov/finaid/prof/resources/data/pell-2005-06/eoy-05-06.pdf). Suppose that this result
According to a 2011 poll, 55% of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Suppose that this result is true for the current population of Americans. a. Let x be a binomial random variable that denotes the number of people in a random sample of 17 Americans
In a poll, men and women were asked, “When someone yelled or snapped at you at work, how did you want to respond?” Twenty percent of the women in the survey said that they felt like crying (Time, April 4, 2011). Suppose that this result is true for the current population of women employees. A
According to a Wakefield Research survey of adult women, 50% of the women said that they had tried five or more diets in their lifetime (USA TODAY, June 21, 2011). Suppose that this result is true for the current population of adult women. A random sample of 13 adult women is selected. Use the
Magnetic resonance imaging (MRI) is a process that produces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to lie within a small, enclosed space during the MRI test. Suppose that 20% of all patients undergoing
In a 2011 Time/Money Magazine survey of adult Americans, 61% said that they were less sure that their children will achieve the American Dream (Time, October 10, 2011). Suppose that this result is true for the current population of adult Americans. A random sample of 16 adult Americans is selected.
During the 2011 NFL regular season, kickers converted 83.5% of the field goals attempted. Assume that this percentage is true for all kickers in the upcoming NFL season. What is the probability that a randomly selected kicker who will try 4 field goal attempts in a game will?a. Convert all 4 field
A professional basketball player makes 85% of the free throws he tries. Assuming this percentage holds true for future attempts, use the binomial formula to find the probability that in the next eight tries, the number of free throws he will make isa. Exactly 8b. Exactly 5
Although Microsoft Windows is the primary operating system for desktop and laptop PC computers, Microsoft’s Windows Phone operating system is installed in only 1.6% of smart phones (www. latimes.com/business/la-fi-google-mobile-20110817,0,6230477.story). a. Assuming that 1.6% of all current smart
An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of the people who used the shredder were satisfied with it.Because of this high acceptance rate, the company decided to market the new shredder. Assume that 80% of all people
Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees a refund or a replacement for any calculator that malfunctions within 2 years from the date of purchase. It is known from past data that despite all
A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this
Explain the meaning of the probability distribution of a discrete random variable. Give one example of such a probability distribution. What are the three ways to present the probability distribution of a discrete random variable?
Explain the hypergeometric probability distribution. Under what a condition is this probability distribution applied to find the probability of a discrete random variable x? Give one example of the application of the hypergeometric probability distribution.
Let N = 8, r = 3, and n = 4. Using the hypergeometric probability distribution formula, finda. P(x = 2)b. P(x = 0)c. P(x < 1)
Let N = 14, r = 6, and n = 5. Using the hypergeometric probability distribution formula, finda. P(x = 4)b. P(x = 5)c. P(x < 1)
Let N = 11, r = 4, and n = 4. Using the hypergeometric probability distribution formula, finda. P(x = 2)b. P(x = 4)c. P(x < 1)
Let N = 16, r = 10, and n = 5. Using the hypergeometric probability distribution formula, finda. P(x = 5)b. P(x = 0)c. P(x < 1)
An Internal Revenue Service inspector is to select 3 corporations from a list of 15 for tax audit purposes. Of the 15 corporations, 6 earned profits and 9 incurred losses during the year for which the tax returns are to be audited. If the IRS inspector decides to select 3 corporations randomly,
Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They
A really bad carton of 18 eggs contains 7 spoiled eggs. An unsuspecting chef picks 4 eggs at random for his “Mega-Omelet Surprise.” Find the probability that the number of unspoiled eggs among the 4 selected isa. Exactly 4b. 2 or fewerc. More than 1
Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5
What are the conditions that must be satisfied to apply the Poisson probability distribution?
Briefly explain the two characteristics (conditions) of the probability distribution of a discrete random variable.
Using the Poisson formula, find the following probabilities.a. P(x < 1) for λ = 5b. P(x = 2) for λ = 2.5Verify these probabilities using Table III of Appendix C.
Using the Poisson formula, find the following probabilities.a. P(x < 2) for λ = 3b. P(x = 8) for λ = 5.5Verify these probabilities using Table III of Appendix C.
Let x be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of x for each of the following. Find the mean, variance, and standard deviation for each of these probability distributions. Draw a graph for each of these probability distributions.a. λ=
Let x be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of x for each of the following. Find the mean, variance, and standard deviation for each of these probability distributions. Draw a graph for each of these probability distributions.a. λ =
A household receives an average of 1.7 pieces of junk mail per day. Find the probability that this household will receive exactly 3 pieces of junk mail on a certain day. Use the Poisson probability distribution formula.
A commuter airline receives an average of 9.7 complaints per day from its passengers. Using the Poisson formula, find the probability that on a certain day this airline will receive exactly 6 complaints.
On average, 5.4 shoplifting incidents occur per week at an electronics store. Find the probability that exactly 3 such incidents will occur during a given week at this store.
On average, 12.5 rooms stay vacant per day at a large hotel in a city. Find the probability that on a given day exactly 3 rooms will be vacant. Use the Poisson formula.
A university police department receives an average of 3.7 reports per week of lost student ID cards.a. Find the probability that at most 1 such report will be received during a given week by this police department. Use the Poisson probability distribution formula.b. Using the Poisson probabilities
Each of the following tables lists certain values of x and their probabilities. Verify whether or not each represents a valid probability distribution and explain why. a. x P(x) 0.... .10 1.... .05 2.... .45 3.... .40 b. x P(x) 2.... .35 3.... .28 4.... .20 5....
A large proportion of small businesses in the United States fail during the first few years of operation. On average, 1.6 businesses file for bankruptcy per day in a particular large city. a. Using the Poisson formula, find the probability that exactly 3 businesses will file for bankruptcy on a
Despite all efforts by the quality control department, the fabric made at Benton Corporation always contains a few defects. A certain type of fabric made at this corporation contains an average of .5 defects per 500 yards. a. Using the Poisson formula, find the probability that a given piece of 500
The number of students who log in to a randomly selected computer in a college computer lab follows a Poisson probability distribution with a mean of 19 students per day.a. Using the Poisson probability distribution formula, determine the probability that exactly 12 students will log in to a
According to a study performed by the NCAA, the average rate of injuries occurring in collegiate women’s soccer is 8.6 per 1000 participants (www.fastsports.com/tips/tip12/).a. Using the Poisson formula, find the probability that the number of injuries in a sample of 1000 women’s soccer
Although Borok’s Electronics Company has no openings, it still receives an average of 3.2 unsolicited applications per week from people seeking jobs.a. Using the Poisson formula, find the probability that this company will receive no applications next week.b. Let x denote the number of
An insurance salesperson sells an average of 1.4 policies per day.a. Using the Poisson formula, find the probability that this salesperson will sell no insurance policy on a certain day.b. Let x denote the number of insurance policies that this salesperson will sell on a given day. Using the
An average of .8 accidents occurs per day in a particular large city.a. Find the probability that no accident will occur in this city on a given day.b. Let x denote the number of accidents that will occur in this city on a given day. Write the probability distribution of x.c. Find the mean,
On average, 20 households in 50 own answering machines.a. Using the Poisson formula, find the probability that in a random sample of 50 households, exactly 25 will own answering machines.b. Using the Poisson probabilities table, find the probability that the number of households in 50 who own
Twenty percent of the cars passing through a school zone are exceeding the speed limit by more than 10 mph.a. Using the Poisson formula, find the probability that in a random sample of 100 cars passing through this school zone, exactly 25 will exceed the speed limit by more than 10 mph.b. Using the
Let x be the number of cars that a randomly selected auto mechanic repairs on a given day. The following table lists the probability distribution of x.Find the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
Each of the following tables lists certain values of x and their probabilities. Determine whether or not each one satisfies the two conditions required for a valid probability distribution and explain why. a. x P(x) 5.... –.36 6.... .48 7.... .62 8.... .26 b. x
Let x be the number of emergency root canal surgeries performed by Dr. Sharp on a given Monday. The following table lists the probability distribution of x.Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
Based on its analysis of the future demand for its products, the financial department at Tipper Corporation has determined that there is a .17 probability that the company will lose $1.2 million during the next year, a .21 probability that it will lose $.7 million, a .37 probability that it will
GESCO Insurance Company charges a $350 premium per annum for a $100,000 life insurance policy for a 40-year-old female. The probability that a 40-year-old female will die within 1 year is .002.a. Let x be a random variable that denotes the gain of the company for next year from a $100,000 life
Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age. The probability is .04 that any weaving machine will break down at any time. Find the probability that at any given timea. All eight weaving machines will be broken downb. Exactly two weaving machines will be
At the Bank of California, past data show that 8% of all credit card holders default at some time in their lives. On one recent day, this bank issued 12 credit cards to new customers. Find the probability that of these 12 customers, eventuallya. Exactly 3 will defaultb. Exactly 1 will defaultc.
Maine Corporation buys motors for electric fans from another company that guarantees that at most 5% of its motors are defective and that it will replace all defective motors at no cost to Maine Corporation. The motors are received in large shipments. The quality control department at Maine
One of the toys made by Dillon Corporation is called Speaking Joe, which is sold only by mail. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees a refund or a replacement for any Speaking Joe toy if the chip that is installed inside becomes
In a list of 15 households, 9 own homes and 6 do not own homes. Four households are randomly selected from these 15 households. Find the probability that the number of households in these 4 who own homes isa. Exactly 3b. At most 1c. Exactly 4
Twenty corporations were asked whether or not they provide retirement benefits to their employees. Fourteen of the corporations said they do provide retirement benefits to their employees, and 6 said they do not. Five corporations are randomly selected from these 20. Find the probability thata.
Uniroyal Electronics Company buys certain parts for its refrigerators from Bob’s Corporation. The parts are received in shipments of 400 boxes, each box containing 16 parts. The quality control department at Uniroyal Electronics first randomly selects 1 box from each shipment and then randomly
Multiple choice questions:1. For the probability distribution of a discrete random variable, the probability of any single value of x is alwaysa. in the range 0 to 1b. 1.0c. less than zero2. For the probability distribution of a discrete random variable, the sum of the
Briefly explain when a hypergeometric probability distribution is used. Give one example of a hypergeometric probability distribution.
Describe the three conditions that must be satisfied to apply the Poisson probability distribution.
Let x be the number of homes sold per week by all four real estate agents who work at a realty office. The following table lists the probability distribution of x.Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
According to a survey, 60% of adults believe that all college students should be required to perform a specified number of hours of community service to graduate. Assume that this percentage is true for the current population of all adults.a. Find the probability that the number of adults in a
The Red Cross honors and recognizes its best volunteers from time to time. One of the Red Cross offices has received 12 nominations for the next group of 4 volunteers to be recognized. Eight of these 12 nominated volunteers are female. If the Red Cross office decides to randomly select 4 names out
The police department in a large city has installed a traffic camera at a busy intersection. Any car that runs a red light will be photographed with its license plate visible, and the driver will receive a citation. Suppose that during the morning rush hour of weekdays, an average of 10 drivers are
The binomial probability distribution is symmetric when p = .50, it is skewed to the right when p < .50, and it is skewed to the left when p > .50. Illustrate these three cases by writing three probability distributions and graphing them. Choose any values of n (4 or higher) and p and use the
State the four conditions of a binomial experiment. Give one example of such an experiment.
For the standard normal distribution, find the area within one standard deviation of the mean—that is, the area between μ − σ and μ + σ
Alpha Corporation is considering two suppliers to secure the large amounts of steel rods that it uses. Company A produces rods with a mean diameter of 8 mm and a standard deviation of .15 mm and sells 10,000 rods for $400. Company B produces rods with a mean diameter of 8 mm and a standard
A gambler is planning to make a sequence of bets on a roulette wheel. Note that a roulette wheel has 38 numbers, of which 18 are red, 18 are black, and 2 are green. Each time the wheel is spun, each of the 38 numbers is equally likely to occur. The gambler will choose one of the following two
A charter bus company is advertising a singles outing on a bus that holds 60 passengers. The company has found that, on average, 10% of ticket holders do not show up for such trips; hence, the company routinely overbooks such trips. Assume that passengers act independently of one another.a. If the
The amount of time taken by a bank teller to serve a randomly selected customer has a normal distribution with a mean of 2 minutes and a standard deviation of .5 minute.a. What is the probability that both of two randomly selected customers will take less than 1 minutes each to be served?b. What is
Suppose you are conducting a binomial experiment that has 15 trials and the probability of success of .02. According to the sample size requirements, you cannot use the normal distribution to approximate the binomial distribution in this situation. Use the mean and standard deviation of this
A variation of a roulette wheel has slots that are not of equal size. Instead, the width of any slot is proportional to the probability that a standard normal random variable z takes on a value between a and (a + .1), where a = –3.0, –2.9, –2.8, . . . , 2.9, 3.0. In other words, there are
Refer to Exercise 6.98. In that exercise, suppose the mean is set to be 8 ounces, but the standard deviation is unknown. The cups used in the machine can hold up to 8.2 ounces, but these cups will overflow if more than 8.2 ounces is dispensed by the machine. What is the smallest possible standard
For the standard normal distribution, find the area within 1.5 standard deviations of the mean—that is, the area between μ – 1.5σ and μ + 1.5σ
For the standard normal distribution, what is the area within two standard deviations of the mean?
For the standard normal distribution, what is the area within 2.5 standard deviations of the mean?
For the standard normal distribution, what is the area within three standard deviations of the mean?
Find the area under the standard normal curve a. Between z = 0 and z = 1.95 b. Between z = 0 and z = –2.05 c. Between z = 1.15 and z 2.37 d. From z = 1.53 to z = –2.88 e. From z = –1.67 to z = 2.24
Find the area under the standard normal curve a. From z = 0 to z = 2.34 b. Between z = 0 and z = –2.58 c. From z = .84 to z = 1.95 d. Between z = –.57 and z = –2.49 e. Between z = 2.15 and z = 1.87

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