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statistics

Questions and Answers of Statistics

Suppose that an automobile parts wholesaler claims that .5 percent of the car batteries in a shipment are defective. A random sample of 200 batteries is taken, and four are found to be defective. (1)
Suppose that x has a hypergeometric distribution with, , and . Find:a. p ( x = 0)b. p ( x = 1)c. p ( x = 2)d. p ( x = 3)e. p ( x = 4)f. p ( x ≥ 2)g. p ( x < 3)h. p ( x > 1)
Suppose that x has a hypergeometric distribution with n = 8,r =5 and n = 4. Finda. Write out the probability distribution of x.b. Find the mean variance and standard deviation of this distribution.
Among 12 metal parts produced in a machine shop, 3 are defective. If a random sample of three of these metal parts is selected, find:a. The probability that this sample will contain at least two
Suppose that you purchase (randomly select) 3 TV sets from a production run of 10 TV sets. Of the 10 TV sets, 9 are destined to last at least five years without needing a single repair. What is the
Suppose that you own a car dealership and purchase (randomly select) 7 cars of a certain make from a production run of 200 cars. Of the 200 cars, 160 are destined to last at least five years without
Let x be the yearly proportional return for stock C, and let y be the yearly proportional return for stock D. If µx =11, µy =09, σx =17, σy =17, and σ2xy =0412, find the mean and standard
Below we give a joint probability table for two utility bonds where the random variable x represents the percentage return for bond 1 and the random variable y represents the percentage return for
A rock concert promoter has scheduled an outdoor concert on July 4th. If it does not rain, the promoter will make $ 30,000. If it does rain, the promoter will lose $ 15,000 in guarantees made to the
The demand (in number of copies per day) for a city newspaper, x, has historically been 50,000, 70,000, 90,000, 110,000, or 130,000 with the respective probabilities .1, .25, .4, .2, and .05.a. Graph
United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to eight randomly
A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable
Aretail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store’s goal is to cash no more than eight bad checks per week. The average number of
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson process with an average of 1.5 accidents every three months. During the last three months, four
A high- security government installation has installed four security systems to detect attempted break-ins. The four security systems operate independently of each other, and each has a .85
A new stain removal product claims to completely remove the stains on 90 percent of all stained garments. Assume that the product will be tested on 20 randomly selected stained garments, and let x
A state has averaged one small business failure per week over the past several years. Let x denote the number of small business failures in the next eight weeks. Use the Poisson distribution to find
A candy company claims that its new chocolate almond bar averages 10 almonds per bar. Let x denote the number of almonds in the next bar that you buy. Use the Poisson distribution to find p (x ≤ 4)
Describe how to compute the mean (or expected value) of a discrete random variable, and interpret what this quantity tells us about the observed values of the random variable.
Describe how to compute the standard deviation of a discrete random variable, and interpret what this quantity tells us about the observed values of the random variable.
Recall from Example 5.5 that Sound City also sells the ClearTone- 400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 6 weeks with no radios sold, 30 weeks
Use the estimated probability distribution in Exercise 5.8 to calculate μ σ2x , and. σx
Consider the figure given in the margin. Find the value k that makes the function f(x) a valid continuous probability distribution.
Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Further-more, suppose that historical flight records indicate that the actual flight time between the two
Refer to Exercise 6.11. a. Calculate the mean flight time and the standard deviation of the flight time. b. Find the probability that the flight time will be within one standard deviation of the
Consider the figure given in the margin. Find the value c that makes the function f(x) a valid continuous probability distribution.
A weather forecaster predicts that the May rainfall in a local area will be between three and six inches but has no idea where within the interval the amount will be. Let x be the amount of May
Refer to Exercise 6.14 and find the probability that the observed May rainfall will fall within two standard deviations of the mean May rainfall.
Explain what the mean, μ, tells us about a normal curve, and explain what the standard deviation, σ, tells us about a normal curve.
In each case, sketch the two specified normal curves on the same set of axes:a. A normal curve with μ = 20 and σ = 3, and a normal curve with μ = 20 and σ = 6.b. A normal curve with μ = 20 and
Let x be a normally distributed random variable having mean μ = 30 and standard deviation σ = 5. Find the z value for each of the following observed values of x: a. x = 25 b. x = 15 c. x = 30
If the random variable z has a standard normal distribution, sketch and find each of the following probabilities:a. P(0 ≤ z ≤ 1.5)b. P(z ≥ 2)c. P(z ≤ 1.5)d. P(z ≥ – 1)e. P(z ≤ – 3)f.
Suppose that the random variable z has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point. a. z .01 b. z .05 c. z .02 d. – z
Suppose that the random variable x is normally distributed with mean m 1,000 and standard deviation s 100. Sketch and find each of the following probabilities:a. P(1,000 ≤ x ≤ 1,200)b. P(x >
Suppose that the random variable x is normally distributed with mean μ = 500 and standard deviation σ = 100. For each of the following, use the normal table to find the needed value k. In each
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16.a. Sketch the distribution of Stanford–Binet IQ test scores.b. Write the equation
Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. a. What is the probability that weekly demand
The lifetimes of a particular brand of DVD player are normally distributed with a mean of eight years and a standard deviation of six months. Find each of the following probabilities where x denotes
United Motors claims that one of its cars, the Starbird 300, gets city driving mileages that are normally distributed with a mean of 30 mpg and a standard deviation of 1 mpg. Let x denote the city
An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent. On the other
A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.95 ounces and 16.05 ounces. A jar is selected from the process
A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean
Recall from Exercise 6.28 that yearly returns on common stocks are normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. a. What percentage of yearly returns are
Two students take a college entrance exam known to have a normal distribution of scores. The students receive raw scores of 63 and 93, which correspond to z scores (often called the standardized
In the book Advanced Managerial Accounting, Robert P. Magee discusses monitoring cost variances. A cost variance is the difference between a budgeted cost and an actual cost. Magee considers weekly
Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $ 3,000 and a standard deviation of $ 500. An insurance company has decided to
Suppose that the 33rd percentile of a normal distribution is equal to 656 and that the 97.5th percentile of this normal distribution is 896. Find the mean m and the standard deviation s of the normal
Explain how we make a continuity correction. Why is a continuity correction needed when we approximate a binomial distribution by a normal distribution?
Suppose that x has a binomial distribution with n = 200 and p = .4.a. Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.b. Make
Is the height of a probability curve over a given point a probability? Explain.
Repeat Exercise 6.39 with n = 200 and p = .5.In exercise Suppose that x has a binomial distribution with n = 200 and p = .4.a. Show that the normal approximation to the binomial can appropriately be
An advertising agency conducted an ad campaign aimed at making consumers in an Eastern state aware of a new product. Upon completion of the campaign, the agency claimed that 20 percent of consumers
In order to gain additional information about respondents, some marketing researchers have used ultraviolet ink to precode questionnaires that promise confidentiality to respondents. Of 205 randomly
When a store uses electronic article surveillance (EAS) to combat shoplifting, it places a small sensor on each item of merchandise. When an item is legitimately purchased, the sales clerk is
A department store will place a sale item in a special display for a one- day sale. Previous experience suggests that 20 percent of all customers who pass such a special display will purchase the
State the formula for the exponential probability curve. Define each symbol in the formula.
Suppose that the random variable x has an exponential distribution with 2. a. Write the formula for the exponential probability curve of x. What are the possible values of x? b. Sketch the
Repeat Exercise 6.48 with λ= 3In Exercise 6.48Suppose that the random variable x has an exponential distribution with 2.a. Write the formula for the exponential probability curve of x. What are the
When is it appropriate to use the uniform distribution to describe a random variable x?
Recall in Exercise 5.32 that the number of customer arrivals at a bank’s drive- up window in a 15- minute period is Poisson distributed with a mean of seven customer arrivals per 15- minute period.
The length of a particular telemarketing phone call, x, has an exponential distribution with mean equal to 1.5 minutes.a. Write the formula for the exponential probability curve of x.b. Sketch the
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson distribution with an average of one accident per month. Let x denote the time (in months) between
Discuss how a normal probability plot is constructed.
Consider the sample of 12 incomes given in Example 3.2 (page 103).a. Sort the income data from smallest to largest, and compute i (n 1) for each observation.b. Compute the standardized normal
Consider the 20 DVD satisfaction ratings given on page 121. Construct a normal probability plot for these data and interpret the plot
Anormal probability plot can be constructed using MINITAB. Use the selections Stat: Basic Statistics: Normality test, and select the data to be analyzed. Although the MINITAB plot is slightly
In a bottle- filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. Bottles containing less than 15.95 oz do
Suppose that the random variable x has a uniform distribution with c = 2 and d = 8.a. Write the formula for the probability curve of x, and write an interval that gives the possible values of x.b.
In a murder trial in Los Angeles, a shoe expert stated that the range of heights of men with a size 12 shoe is 71 inches to 76 inches. Suppose the heights of all men wearing size 12 shoes are
In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance. a. If IQ test scores are normally distributed with mean 100 and standard deviation 16, what percentage
The amount of sales tax paid on a purchase is rounded to the nearest cent. Assume that the round-off error is uniformly distributed in the interval .5 to .5 cent.a. Write the formula for the
A consensus forecast is the average of a large number of individual analysts’ forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 5.0
Recall from Exercise 6.63 that individual forecasts of a particular interest rate are normally distributed with a mean of 5 percent and a standard deviation of 1.2 percent.a. What percentage of
The scores on the entrance exam at a well- known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. At what value should the lowest passing
A machine is used to cut a metal automobile part to its desired length. The machine can be set so that the mean length of the part will be any value that is desired. The standard deviation of the
A motel accepts 325 reservations for 300 rooms on July 1, expecting 10 percent no- shows on average from past records. Use the normal approximation to the binomial to find the probability that all
Suppose a software company finds that the number of errors in its software per 1,000 lines of code is described by a Poisson distribution. Furthermore, it is found that there is an average of four
For each investment class in Table 3.9 (page 139), assume that future returns are normally distributed with the population mean and standard deviation given in Table 3.9. Based on this assumption:a.
The daily water consumption for an Ohio community is normally distributed with a mean consumption of 800,000 gallons and a standard deviation of 80,000 gallons. The community water system will
Suppose the times required for a cable company to fix cable problems in its customers’ homes are uniformly distributed between 10 minutes and 25 minutes. What is the probability that a randomly
Suppose the waiting time to get food after placing an order at a fast- food restaurant is exponentially distributed with a mean of 60 seconds. If a randomly selected customer orders food at the
Net interest margin— often referred to as spread— is the difference between the rate banks pay on deposits and the rate they charge for loans. Suppose that the net interest margins for all U. S.
In an article in Advertising Age, Nancy Giges studies global spending patterns. Giges presents data concerning the percentage of adults in various countries who have purchased various consumer items
Assume that the ages for first marriages are normally distributed with a mean of 26 years and a standard deviation of 4 years. What is the probability that a person getting married for the first time
Assume that the waiting time x for an elevator is uniformly distributed between zero and six minutes.a. Write the formula for the probability curve of x.b. Graph the probability curve of x.c. Find
Refer to Exercise 6.8. a. Calculate the mean, μx, the variance, σ2x, and the standard deviation, σx. b. Find the probability that the waiting time of a randomly selected patron will be within one
Marketing researchers often use city blocks as clusters in cluster sampling. Using this fact, explain how a market researcher might use multistage cluster sampling to select a sample of consumers
Explain: a. Three types of surveys and discuss their advantages and disadvantages. b. Three types of survey questions and discuss their advantages and disadvantages.
A company that produces and markets video game systems wishes to assess its customers’ level of satisfaction with a relatively new model, the XYZ- Box. In the six months since the introduction of
Explain each of the following terms: a. Undercoverage b. Nonresponse c. Response bias
A market research firm sends out a Web- based survey to assess the impact of advertisements placed on a search engine’s results page. About 65% of the surveys were answered and sent back. What
Acompany that sells and installs custom designed home theatre systems claims to have sold 977 such systems last year. In order to assess whether these claimed sales are valid, an accountant numbers
Recall that the trash bag manufacturer has concluded that its new 30- gallon bag will be the strongest such bag on the market if its mean breaking strength is at least 50 pounds. In order to provide
The year 1987 featured extreme volatility on the stock market, including a loss of over 20 percent of the market’s value on a single day. Figure 7.6 (a) shows the percent frequency histogram of the
Suppose that we wish to assess whether more than 60 percent of all U. S. households in a particular income class bought life insurance last year. That is, we wish to assess whether p, the proportion
A computer supply house receives a large shipment of flash drives each week. Past experience has shown that the number of flaws (bad sectors) per flash drive is either 0, 1, 2, or 3 with
Each day a manufacturing plant receives a large shipment of drums of Chemical ZX- 900. These drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to
Suppose that we will take a random sample of size n from a population having mean µ and standard deviation s. For each of the following situations, find the mean, variance, and standard deviation of
Discuss how we select a random sample.

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