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Question: Find the area under the standard normal


Find the area under the standard normal curve to the right of
(a) z = 1.27
(b) z = .54
(c) z = -1 .63
( d) z = -1.325 (interpolate)


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> Explain why nations trade, and describe how international trade is measured. (1) Would it be wise for an advertising agency to open offices in Europe and Asia to service a single multinational client? Why or why not? (2) If IBM invests $40 million in a j

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> Identify four fundamental consumer rights and the responsibility of business to respect them. Is there a point at which responsibility for product safety shifts from the seller to the buyer? Explain your answer.

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> Explain the major functions of the Federal Reserve System, and identify other key federal financial institutions. (1) Why does the Fed want to avoid an “overheating” economy? (2) Why is the Fed’s discount window considered the “lender of last resort” for

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> Describe the two options for equity financing, and explain how companies prepare an initial public offering. (1) High-tech firms tend to dominate IPO filings year after year; why do you suppose this is so? (2) Why does the volume of IPOs tend to track th

> Identify the major categories of long-term debt financing. (1) How could rates of technological change affect a company’s decision about whether to buy or lease equipment, vehicles, and other assets? (2) Why would lenders want to see that a business alre

> Identify the major categories of short-term debt financing. (1) How does getting a secured loan using accounts receivable as collateral differ from factoring? (2) Why would any seller offer trade financing, since it ties up working capital without genera

> Compare the advantages and disadvantages of debt and equity financing, and explain the two major considerations in choosing from financing alternatives. (1) What factors might lead a company to gain additional funds through debt financing rather than thr

> Identify four macroeconomic issues that are essential to understanding the behavior of the economy. (1) Are colleges and universities an example of pure competition or monopolistic competition? Why? (2) Are monopolies always harmful to consumers? Why or

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> The three finalists for an award are A, B, and C. They are rated by two judges. Each judge assigns the ratings 1 for best, 2 for intermediate, and 3 for worst. Let X denote the total score for finalist A (the sum of the ratings received from the two ju

> For a standard normal variable, Z, find (a) P(Z < .73) (b) P(Z < -.73) (c) P(Z > 1.42) (d) P(Z > -1.42) (e) P(-1.4 < Z < 2.57) (f) P( .07 < Z < .70 ) (g) P(-1.65 < Z < -.45) (h) P(|Z| < 1.96)

> Determine the following probabilities from the curve f ( x) diagrammed in Exercise 6.1 (a). (a) P( 0 (b) P(l.8 (c) P(.4 (d) P[ X = 1] Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous

> Identify the z values in the following diagrams of the standard normal distribution (interpolate, as needed)

> Identify the z values in the following diagrams of the standard normal distribution (interpolate, as needed).

> Find the area under the standard normal curve over the interval (a) z = -.44 to z = .44 (b) z = -1.33 to z = 1.33 (c) z = .40 to z = 2.03 (d) z = 1.405 to z = 2.306 (interpolate)

> Find the area under the standard normal curve over the interval (a) z = - .85 to z = .85 (b) z = -1.15 to z = 1.15 (c) z = .58 to z = 2.03 (d) z = -.845 to z = 1.366 (interpolate) (e) Check all of your answers using software.

> Find the area under the standard normal curve to the right of (a) z = .63 (b) z = 2.63 (c) z = -1.23 (d) z = 1.635 (interpolate)

> Find the area under the standard normal curve to the left of (a) z = 1.63 (b) z = 1.07 (c) z = -1.07 (d) z = -1.55

> Find the area under the standard normal curve to the left of (a) z = 1.37 (b) z = .34 (c) z = -1.61 (d) z = -2.53

> Faced with a tight deadline on two major projects, you decide to hire two of the five available persons to help complete the work. They have 2, 3, 5, 3, and 2 years experience, respectively. Since their references are very similar, you decide to select t

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> Males 20 to 29 years old have a mean height of 69.4 inches with a standard deviation of 3.5 inches. Females 20 to 29 years old have a mean h eight of 64.1 inches with a standard deviation of 3.1 inches. (a) Find the standardized variable for the heights

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> According to a recent Federal Trade Commission Report, about .13% of the persons in the 20-29 year old age group filed identity theft complaints. From a random sample of n = 600 persons 20-29 years old, let X denote the number who filed an identity theft

> Records over several years show that the probability is .00003 that a car will have a flat tire while driving through a long tunnel. About 16,000 cars use the tunnel each week. Determine the probability that 2 or more cars will have a flat next week (a)

> For health reasons, homes need to be inspected for radon gas that decays and produces alpha particles. One device counts the number of alpha particles that hit its detector. To a good approximation, in one area, the count for the next week follows a Pois

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> Th e number of weekly breakdowns of a department's computing system is a random variable having a Poisson distribution with m = .4. What is the probability the computer will run for two consecutive weeks without a breakdown?

> A Poisson distribution with m = 5.5 governs the daily number of insurance claims handled by an adjuster. Det ermine the probability that she handles (a) 6 claims tomorrow. (b) 12 claims in the next two days. (c) 3 or fewer tomorrow.

> A child psychologist interested in how friends are selected studies groups of three children. For one group, Ann, Barb, and Carol, each is asked which of the other two she likes best. (a) Make a list of the outcomes. (b) Let X be the number of times Car

> Refer to Exercise 5.78. (a) What are the unusual values for the number of underweight hamburgers in the sample if they correspond to proportions outside of the control limits of the p-chart? (b) Use the binomial table to find th e probability of observ

> Several fast food restaurants advertise quarter-pound hamburgers. This could be interpreted as meaning half the hamburgers made have an uncooked weight of at least a quarter-pound and half have a weight that is less. An inspector checks 20 uncooked hambu

> Refer to the credit card application approval process. (a) Make a p-chart using the centerline and control limits calculated for Po = .4. (b) Suppose the next five weeks bring 12, 10, 15, 11, and 16 applications requiring full review. Graph the correspon

> Refer to the credit card application approval process where unusual values are defined. (a) Show that if 4 is included as an unusual value, then the probability P [ X ≤ 4 or X ≥ 13 ) is greater than .05. (b) Show that if 12 is included as an unusual va

> Many computer packages produce binomial probabilities. We illustrate the MINITAB commands for obtaining the binomial probabilities with n = 5 and p = .33. The probabilities P [ X = x] are obtained by first setting 0, 1, 2, 3, 4, 5 in Cl and then selectin

> The following table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. For each part below, find the mean and standard deviation of the specified random variable. (a) X stands

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> Referring to Exercise 5.71, find: (a) The expected number of college seniors, in a random sample of 20, supporting the increased funding. (b) The probability that the number of sampled college seniors supporting the increased funding equals the expecte

> Suppose that 20% of the college seniors support an increase in federal funding for care of the elderly. If 20 college seniors are randomly selected, what is the probability that at most 3 of them support the increased funding?

> (a) For the binomial distribution with n = 3 and p = .6, list the probability distribution ( x, f ( x)) in a table. (b) From this table, calculate the mean and standard deviation by using the methods of Section 3. (c) Check your results with the formula

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> A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that: (a) Fewer than 14 of them have had a physical examination in th

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> According to the U.S. Census Bureau, about 10% of persons between 25 and 29 years old live alone. For a random sample of size n, use the binomial table, or software, to find the probability of (a) l or fewer persons living alone when n 14. (b) 2 or mor

> Using the binomial table, find the probability of: (a) Four successes in 13 trials when p = .3. (b) Eight failures in 13 trials when p = . 7. (c) Eight successes in 13 trials when p = .3. Explain why you get identical answers in parts (b) and ( c).

> Rh-positive blood appears in 85% of the white population in the United States. If 8 people are sampled at random from that population, find the probability that: (a) At least 6 of them have Rh-positive blood. (b) At most 3 of them have Rh-negative bloo

> Suppose 15% of the trees in a forest have severe leaf damage from air pollution. If 5 trees are selected at random, find the probability of: (a) Three of the selected trees h ave severe leaf damage. (b) No more than two h ave severe leaf damage.

> According to a recent survey, outside of their own family members, 26% of adult Americans have no close friend to confide in. If this is the prevailing probability today, find the probability that in a random sample of n = 5 adults (a) Two or more have

> About 75% of dog owners buy holiday presents for their dogs. Suppose n = 4 dog owners are randomly selected. Find the probability of: (a) Three or more buy their dog holiday presents. (b) At most three buy their dog holiday presents. (c) Find the expe

> Refer to Exercise 5.59. What is the most probable value of X ( called the mode of a distribution)? Data from Exercise 5.59: An interior designer makes a presentation to potential clients and this results in sales of h er services in 25% of the cases. Le

> Two brands of beverages, B and M, are popular with students. The owner of one campus establishment observes sales and, for each of three weekends, records which brand has the highest sales. List the possible outcomes, and for each outcome record the numb

> An interior designer makes a presentation to potential clients and this results in sales of h er services in 25% of the cases. Let X denote the number of sales in the next four presentations. Assuming the results for different clients are independent, ca

> (a) Plot the probability histograms for the binomial distributions for n = 5 and p equal to .2, .5, and .8. (b) Locate the means. (c) Find P [ X ≥ 4 ) for each of the three cases.

> In each case, find the probability of x successes in n Bernoulli trials with success probability p for each trial. (a) X = 2 n = 3 p = .35 (b) X = 3 n = 6 p = .25 (c) X = 2 n = 6 p = .65

> Construct a tree diagram for three Bernoulli trials. Attach probabilities in terms of p and q to each outcome and then table the binomial distribution for n = 3.

> For each situation, state whether or not a binomial distribution holds for the random variable X. Also, identify the numerical values of n and p when a binomial distribution holds. (a) A fair die is rolled 10 times, and X denotes the number of times 6 s

> The accompanying table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. Suppose that the selection of a person is considered a trial and the presence of the allergy is consi

> An animal either dies (D) or survives (S) in the course of a surgical experiment. The experiment is to be performed first with two animals. If both survive, no further trials are to be made. If exactly one animal survives, one more animal is to undergo t

> A graphic designer makes a presentation to clients and this results in sales of her services in one-fourth of the cases. Assuming the results for different clients are independent. (a) Find the probability that exactly 3 of the next 4 presentations resul

> According to a recent survey, about 40% of adults reported that the most helpful method to achieve a goal is to share their goal with friends and ask them for support. Let S be the event that an adult feels sharing with friends is the most helpful method

> According to numbers provided by the Bureau of Labor Statistics, the probability that three unrelated new businesses will last for five years is .216. What is the probability that all three have failed before that time? Assume that the conditions for Ber

> Refer to Exercise 5.4. Suppose instead there are two finalists A and B and four judges. Each judge assigns the ratings 1 for the best and 2 for the worst finalists. (a) List all possible assignments of ratings to finalist A by the four judges. (b) List

> Consider Bernoulli trials with success probability p = .3. (a) Find the probability that four trials result in all failures. (b) Given that the first four trials result in all failures, what is the conditional probability that the next four trials are al

> A backpacking party carries three emergency signal flares, each of which lights with a probability of .94. Assuming that the flares operate independently, find: (a) The probability that at least one flare lights. (b) The probability that exactly two fl

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> Refer to Exercise 5.45. Now suppose for each plot a fair coin is tossed. If a head shows up, the plot is treated; otherwise, it is a control. With this manner of treatment allocation, answer parts (a) and (b). Data from Exercise 5.45: From four agricult

2.99

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