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Complete Business Statistics 7th Edition Amir Aczel, Jayavel Sounderpandian - Solutions
Light bulbs manufactured by a particular company have an exponentially distributed life with mean 100 hours.a. What is the probability that the light bulb I am now putting in will last at least 65 hours?b. What is the standard deviation of the lifetime of a light bulb?
The Bombay Company offers reproductions of classic 18th- and 19th-century English furniture pieces, which have become popular in recent years. The following table gives the probability distribution of the number of Raffles tables sold per day at a particular Bombay store.Number of
According to an article in USA Today, 90% of Americans will suffer from high blood pressure as they age. Out of 20 randomly chosen people what is the probability that at most 3 will suffer from high blood pressure?
The number of orders for installation of a computer information system arriving at an agency per week is a random variable X with the following probability distribution: x P(x)0 .......0.101 .......0.202 .......0.303 .......0.154 .......0.155 .......0.056 .......0.05a. Prove that P(X) is a
An article in The New York Times reports that several hedge fund managers now make more than a billion dollars a year. Suppose that the annual income of a hedge fund manager in the top tier, in millions of dollars a year, is given by the following probability distribution: x ($ millions) P(x)$1,700
Consider the situation in the previous problem, and assume that the distribution holds for all weeks throughout the year and that weekly orders are independent from week to week. Let Y denote the number of weeks in the year in which no orders are received (assume a year of 52 weeks). a. What kind
An analyst kept track of the daily price quotation for a given stock. The frequency data led to the following probability distribution of daily stock price: Price x in Dollars P(x) 17 ............ 0.05 17.125 .......... 0.05 17.25 .......... 0.10 17.375 .......... 0.15 17.5 .......... 0.20 17.625
In problem 3-69, suppose that the company makes $1,200 on each order but has to pay a fixed weekly cost of $1,750. Find the expected weekly profit and the standard deviation of weekly profits. x ...... P(x) 0 ....... 0.10 1 ....... 0.20 2 ....... 0.30 3 ....... 0.15 4 ....... 0.15 5 ....... 0.05 6
Out of 140 million cellular telephone subscribers in the United States, 36 million use Verizon.6a. Ten wireless customers are chosen. Under what conditions is the number of Verizon customers a binomial random variable?b. Making the required assumptions above, find the probability that at least two
An advertisement claims that two out of five doctors recommend a certain pharmaceutical product. A random sample of 20 doctors is selected, and it is found that only 2 of them recommend the product. a. Assuming the advertising claim is true, what is the probability of the observed event? b.
Five percent of the many cars produced at a plant are defective. Ten cars made at the plant are sent to a dealership. Let X be the number of defective cars in the shipment.a. Under what conditions can we assume that X is a binomial random variable?b. Making the required assumptions, write the
The time, in minutes, necessary to perform a certain task has the uniform [5, 9] distribution.a. Write the probability density function of this random variable.b. What is the probability that the task will be performed in less than 8 minutes? Explain.c. What is the expected time required to perform
Suppose X has the following probability density function:a. Graph the density function.b. Show that f (x) is a density function.c. What is the probability that X is greater than 5.00?
The number of defects in a machine-made product is a random variable X with the following probability distribution:XP(x)0 .....0.11 .....0.22 .....0.33 .....0.34 .....0.1a. Show that P(x) is a probability distribution.b. Find the probability P(1 < X ≤ 3).c. Find the probability P(1 < X ≤
Recently, the head of the Federal Deposit Insurance Corporation (FDIC) revealed that the agency maintains a secret list of banks suspected of being in financial trouble. The FDIC chief further stated that of the nation's 14,000 banks, 1,600 were on the list at the time. Suppose that, in an effort
An applicant for a faculty position at a certain university is told by the department chair that she has a 0.95 probability of being invited for an interview. Once invited for an interview, the applicant must make a presentation and win the votes of a majority (at least 8) of the department's 14
The ratings of viewership for the three major networks during prime time recently were as follows. Also shown is the proportion of viewers watching each program?a. What is the mean rating given a program that evening?b. How many standard deviations above or below the mean is the rating for each one
A major ski resort in the eastern United States closes in late May. Closing day varies from year to year depending on when the weather becomes too warm for making and preserving snow. The day in May and the number of years in which closing occurred that day are reported in the table: Day
Ten percent of the items produced at a plant are defective. A random sample of 20 items is selected. What is the probability that more than three items in the sample are defective? If items are selected randomly until the first defective item is encountered, how many items, on average, will have to
Lee Iacocca volunteered to drive one of his Chryslers into a brick wall to demonstrate the effectiveness of airbags used in these cars. Airbags are known to activate at random when the car decelerates anywhere from 9 to 14 miles per hour per second (mph/s). The probability distribution for the
In the previous problem, the time that it takes the airbag to completely fill up from the moment of activation has an exponential distribution with mean 1 second. What is the probability that the airbag will fill up in less than 1/2 second?
The time interval between two successive customers entering a store in a mall is exponentially distributed with a mean of 6.55 seconds.a. What is the probability that the time interval is more than 10 seconds?b. What is the probability that the time interval is between 10 and 20 seconds?c. On a
The Dutch consumer-electronics giant, Philips, is protected against takeovers by a unique corporate voting structure that gives power only to a few trusted shareholders. A decision of whether to sever Philips' links with the loss-producing German electronics firm Grundig had to be made. The
Returns on investments overseas, especially in Europe and the Pacific Rim, are expected to be higher than those of U.S. markets in the near term, and analysts are now recommending investments in international portfolios. An investment consultant believes that the probability distribution of returns
According to a front-page article in The Wall Street Journal, 30% of all students in American universities miss classes due to drinking.8 If 10 students are randomly chosen, what is the probability that at most 3 of them miss classes due to drinking?
According to an article in USA Today, 60% of 7- to 12-year-olds who use the Internet do their schoolwork on line. If 8 kids within this age group who use the Internet are randomly chosen, what is the probability that 2 of them do their schoolwork on line? What is the probability that no more than 5
The cafeteria in a building offers three different lunches. The demands for the three types of lunch on any given day are independent and Poisson distributed with means 4.85, 12.70, and 27.61. The cost of the three types is $12.00, $8.50, and $6.00, respectively. Find the expected value and
The mean time between failures (MTBF) of a hydraulic press is to be estimated assuming that the time between failures (TBF) is exponentially distributed. A foreman observes that the chance that the TBF is more than 72 hours is 50%, and he quotes 72 hours as the MTBF.- Is the foreman right? If not,
An operator needs to produce 4 pins and 6 shafts using a lathe which has 72% chance of producing a defect-free pin at each trial and 65% chance of producing a defect-free shaft at each trial. The operator will first produce pins one by one until he has 4 defect-free pins and then produce shafts one
Hedge funds are institutions that invest in a wide variety of instruments, from stocks and bonds to commodities and real estate. One of the reasons for the success of this industry is that it manages expected return and risk better than other financial institutions. Using the concepts and ideas
Find the following probabilities: P(-1 < Z < 1), P(-1.96 < Z < 1.96), P (-2.33 < Z < 2.33).
Find the probability that a standard normal random variable will be between -0.01 and 0.05.
Find a value such that the probability that the standard normal random variable will be above it is 0.85.
Find z such that P(Z > z) = 0.12.
Find two values, equidistant from 0 on either side, such that the probability that a standard normal random variable will be between them is 0.40.
Find two values of the standard normal random variable, z and – z, such that the two corresponding tail areas of the distribution add to 0.01.
The deviation of a magnetic needle from the magnetic pole in a certain area in northern Canada is a normally distributed random variable with mean 0 and standard deviation 1.00. What is the probability that the absolute value of the deviation from the north pole at a given moment will be more than
For a normal random variable with mean 650 and standard deviation 40, find the probability that its value will be below 600.
Let X be a normally distributed random variable with mean 410 and standard deviation 2. Find the probability that X will be between 407 and 415.
If X is normally distributed with mean 500 and standard deviation 20, find the probability that X will be above 555.
For a normally distributed random variable with mean – 44 and standard deviation 16, find the probability that the value of the random variable will be above 0.
A normal random variable has mean 0 and standard deviation 4. Find the probability that the random variable will be above 2.5.
Let X be a normally distributed random variable with mean µ = 16 and standard deviation σ = 3. Find P(11 < X < 20). Also find P(17 < X < 19) and P(X > 15).
The time it takes an international telephone operator to place an overseas phone call is normally distributed with mean 45 seconds and standard deviation 10 seconds.a. What is the probability that my call will go through in less than 1 minute?b. What is the probability that I will get through in
The number of votes cast in favor of a controversial proposition is believed to be approximately normally distributed with mean 8,000 and standard deviation 1,000. The proposition needs at least 9,322 votes in order to pass. What is the probability that the proposition will pass?
Under the system of floating exchange rates, the rate of foreign money to the U.S. dollar is affected by many random factors, and this leads to the assumption of a normal distribution of small daily fluctuations. The rate of U.S. dollar per euro is believed in April 2007 to have a mean of 1.36 and
Wine Spectator rates wines on a point scale of 0 to 100. It can be inferred from the many ratings in this magazine that the average rating is 87 and the standard deviation is 3 points. Wine ratings seem to follow a normal distribution. In the May 15, 2007, issue of the magazine, the burgudy Domaine
The weights of domestic, adult cats are normally distributed with a mean of 10.42 pounds and a standard deviation of 0.87 pounds. A cat food manufacturer sells three types of foods for underweight, normal, and overweight cats. The manufacturer considers the bottom 5% of the cats underweight and the
According to global analyst Olivier Lemaigre, the average price-to-earnings ratio for companies in emerging markets is 12.5. Assume a normal distribution and a standard deviation of 2.5. If a company in emerging markets is randomly selected, what is the probability that its price-per-earnings ratio
Based on the research of Ibbotson Associates, a Chicago investment firm, and Prof. Jeremy Siegel of the Wharton School of the University of Pennsylvania, the average return on large-company stocks since 1920 has been 10.5% per year and the standard deviation has been 4.75%. Assuming a normal
A manufacturing company regularly consumes a special type of glue purchased from a foreign supplier. Because the supplier is foreign, the time gap between placing an order and receiving the shipment against that order is long and uncertain.This time gap is called "lead time." From past experience,
The daily price of orange juice 30-day futures is normally distributed. In March through April 2007, the mean was 145.5 cents per pound, and standard deviation = 25.0 cents per pound.4 Assuming the price is independent from day to day, find P (x < 100) on the next day.
If X is a normally distributed random variable with mean 120 and standard deviation 44, find a value x such that the probability that X will be less than x is 0.56.
For a normal random variable with mean 16.5 and standard deviation 0.8, find a point of the distribution such that there is a 0.85 probability that the value of the random variable will be above it.
For a normal random variable with mean 19,500 and standard deviation 400, find a point of the distribution such that the probability that the random variable will exceed this value is 0.02.
Find two values of the normal random variable with mean 88 and standard deviation 5 lying symmetrically on either side of the mean and covering an area of 0.98 between them.
For X ~ N(32, 72), find two values x1 and x2, symmetrically lying on each side of the mean, with P(x1 < X < x2) = 0.99.
If X is a normally distributed random variable with mean -61 and standard deviation 22, find the value such that the probability that the random variable will be above it is 0.25.
If X is a normally distributed random variable with mean 97 and standard deviation 10, find x2 such that P(102 < X < x2) = 0.05.
Let X be a normally distributed random variable with mean 600 and variance 10,000. Find two values x1 and x2 such that P(X > x1) = 0.01 and P(X < x2) = 0.05.
Pierre operates a currency exchange office at Orly Airport in Paris. His office is open at night when the airport bank is closed, and he makes most of his business on returning U.S. tourists who need to change their remaining euros back to U.S. dollars. From experience, Pierre knows that the demand
The demand for high-grade gasoline at a service station is normally distributed with mean 27,009 gallons per day and standard deviation 4,530. Find two values that will give a symmetric 0.95 probability interval for the amount of high-grade gasoline demanded daily.
The percentage of protein in a certain brand of dog food is a normally distributed random variable with mean 11.2% and standard deviation 0.6%. The manufacturer would like to state on the package that the product has a protein content of at least x1% and no more than x2%. It wants the statement to
Private consumption as a share of GDP is a random quantity that follows a roughly normal distribution. According to an article in Business Week, for the United States that was about 71%. Assuming that this value is the mean of a normal distribution, and that the standard deviation of the
Find the probability that a standard normal random variable will be between 2 and 3.
The daily price of coffee is approximately normally distributed over a period of 15 days with a mean in April 2007 of $1.35 per pound (on the wholesale market) and standard deviation of $0.15. Find a price such that the probability in the next 15 days that the price will go below it will be 0.90.
The daily price in dollars per metric ton of cocoa in 2007 was normally distributed with µ = $2,014 per metric ton and σ = $2.00. Find a price such that the probability that the actual price will be above it is 0.80.
The manager of a restaurant knows from experience that 70% of the people who make reservations for the evening show up for dinner. The manager decides one evening to overbook and accept 20 reservations when only 15 tables are available. What is the probability that more than 15 parties will show
An advertising research study indicates that 40% of the viewers exposed to an advertisement try the product during the following four months. If 100 people are exposed to the ad, what is the probability that at least 20 of them will try the product in the following four months?Use a normal
According to The Economist, 77.9% of Google stockholders have voting power.7 If 2,000 stockholders are gathered in a meeting, what is the probability that at least 1,500 of them can vote?Use a normal distribution to compute the required probabilities also state the assumptions necessary for a
Sixty percent of the managers who enroll in a special training program will successfully complete the program. If a large company sends 328 of its managers to enroll in the program, what is the probability that at least 200 of them will pass?Use a normal distribution to compute the required
A large state university sends recruiters throughout the state to recruit graduating high school seniors to enroll in the university. University records show that 25% of the students who are interviewed by the recruiters actually enroll. If last spring the university recruiters interviewed 1,889
According to Fortune, Missouri is within 500 miles of 44% of all U.S. manufacturing plants.8 If a Missouri company needs parts manufactured in 122 different plants, what is the probability that at least half of them can be found within 500 miles of the state?Use a normal distribution to compute the
According to Money, 59% of full-time workers believe that technology has lengthened their workday.9 If 200 workers are randomly chosen, what is the probability that at least 120 of them believe that technology has lengthened their workday?Use a normal distribution to compute the required
The time, in hours, that a copying machine may work without breaking down is a normally distributed random variable with mean 549 and standard deviation 68. Find the probability that the machine will work for at least 500 hours without breaking down.
The yield, in tons of ore per day, at a given coal mine is approximately normally distributed with mean 785 tons and standard deviation 60. Find the probability that at least 800 tons of ore will be mined on a given day. Find the proportion of working days in which anywhere from 750 to 850 tons is
Scores on a management aptitude examination are believed to be normally distributed with mean 650 (out of a total of 800 possible points) and standard deviation 50.What is the probability that a randomly chosen manager will achieve a score above 700? What is the probability that the score will be
The price of a share of Kraft stock is normally distributed with mean 33.30 and standard deviation 6. What is the probability that on a randomly chosen day in the period for which our assumptions are made, the price of the stock will be more than $40 per share? Less than $30 per share?
The amount of oil pumped daily at Standard Oil's facilities in Prudhoe Bay is normally distributed with mean 800,000 barrels and standard deviation 10,000. In determining the amount of oil the company must report as its lower limit of daily production, the company wants to choose an amount such
An analyst believes that the price of an IBM stock is a normally distributed random variable with mean $105 and variance 24. The analyst would like to determine a value such that there is a 0.90 probability that the price of the stock will be greater than that value. Find the required value.
Weekly rates of return (on an annualized basis) for certain securities over a given period are believed to be normally distributed with mean 8.00% and variance 0.25. Give two values x1 and x2 such that you are 95% sure that annualized weekly returns will be between the two values.
The impact of a television commercial, measured in terms of excess sales volume over a given period, is believed to be approximately normally distributed with mean 50,000 and variance 9,000,000. Find 0.99 probability bounds on the volume of excess sales that would result from a given airing of the
A travel agency believes that the number of people who sign up for tours to Hawaii during the Christmas-New Year's holiday season is an approximately normally distributed random variable with mean 2,348 and standard deviation 762. For reservation purposes the agency's management wants to find the
A loans manager at a large bank believes that the percentage of her customers who default on their loans during each quarter is an approximately normally distributed random variable with mean 12.1% and standard deviation 2.5%. Give a lower bound x with 0.75 probability that the percentage of people
The power generated by a solar electric generator is normally distributed with mean 15.6 kilowatts and standard deviation of 4.1 kilowatts. We may be 95% sure that the generator will deliver at least how many kilowatts?
Find the probability that a standard normal random variable will be greater in value than -2.33.
Short-term rates fluctuate daily. It may be assumed that the yield for 90-day Treasury bills in early 2007 was approximately normally distributed with mean 4.92% and standard deviation 0.3%. Find a value such that 95% of the time during that period the yield of 90-day T-bills was below this value.
In quality-control projects, engineers use charts where item values are plotted and compared with 3-standard-deviation bounds above and below the mean for the process. When items are found to fall outside the bounds, they are considered nonconforming, and the process is stopped when "too many"
Total annual textbook sales in a certain discipline are normally distributed. Forty-five percent of the time, sales are above 671,000 copies, and 10% of the time, sales are above 712,000 copies. Find the mean and the variance of annual sales.
Typing speed on a new kind of keyboard for people at a certain stage in their training program is approximately normally distributed. The probability that the speed of a given trainee will be greater than 65 words per minute is 0.45. The probability that the speed will be more than 70 words per
The number of people responding to a mailed information brochure on cruises of the Royal Viking Line through an agency in San Francisco is approximately normally distributed. The agency found that 10% of the time, over 1,000 people responds immediately after a mailing, and 50% of the time, at least
The Tourist Delivery Program was developed by several European automakers. In this program, a tourist from outside Europe-most are from the United States-may purchase an automobile in Europe and drive it in Europe for as long as six months, after which the manufacturer will ship the car to the
The number of newspapers demanded daily in a large metropolitan area is believed to be an approximately normally distributed random variable. If more newspapers are demanded than are printed, the paper suffers an opportunity loss, in that it could have sold more papers, and a loss of public
The Federal Funds rate in spring 2007 was approximately normal with µ = 5.25% and σ = 0.05%. Find the probability that the rate on a given day will be less than 1.1%.
Thirty-year fixed mortgage rates in April 2007 seemed normally distributed with mean 6.17%. The standard deviation is believed to be 0.25%. Find a bound such that the probability that the actual rate obtained will be this number or below it is 90%.
A project consists of three phases to be completed one after the other. The duration of each phase, in days, is normally distributed as follows: Duration of Phase I ~ N(84, 32); Duration of Phase II ~ N(102, 42); Duration of Phase III ~ N(62, 22). The durations are independent.a. Find the
The GMAT scores of students who are potential applicants to a university are normally distributed with a mean of 487 and a standard deviation of 98.a. What percentage of students will have scores exceeding 500?b. What percentage of students will have scores between 600 and 700?c. If the university
The profit (or loss) from an investment is normally distributed with a mean of $11,200 and a standard deviation of $8,250.a. What is the probability that there will be a loss rather than a profit?b. What is the probability that the profit will be between $10,000 and $20,000?c. Find x such that the
The weight of connecting rods used in an automobile engine is to be closely controlled to minimize vibrations. The specification is that each rod must be 974 ± 1.2 grams. The half-width of the specified interval, namely, 1.2 grams, is known as the tolerance. The manufacturing process at a plant
A restaurant has three sources of revenue: eat-in orders, takeout orders, and the bar. The daily revenue from each source is normally distributed with mean and standard deviation shown in the table below.a. Will the total revenue on a day be normally distributed?b. What are the mean and standard
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