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 the distinct values of X, the total score of A. Data from Exercise 5.4: 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 judges).
> 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 right of (a) z = 1.27 (b) z = .54 (c) z = -1 .63 ( d) z = -1.325 (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
> Two pieces of wood need to be glued together. After applying glue to both pieces, they must be clamped to obtain the best results. The required clamping time in any application is a random variable. Find the standardized variable Z, for the clamping time
> 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
> Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?
> 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
> A Poisson distribution with m = 2.5 governs the yearly number of tornado touchdowns in a central area of the state. Find the probabilities P [ X ≤ 1 ] and P [ X ≥ 1 ] .
> A Poisson distribution with m = 1.2 governs the number of fireflies that flash in a l O second period during an August evening in the yard. Determine the probability that: (a) 2 fireflies flash. (b) Less than or equal 3 flash . (c) 6 fireflies flash in
> 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
> According to the Mendelian theory of inheritance of genes, offspring of a dihybrid cross of peas could be any of the four types: round-yellow (RY), wrinkled-yellow ( WY), round-green ( RG ) and wrinkled-green ( WG ), and their probabilities are in the ra
> 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
> Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. The type of soft drink purchased in 3 consecutive weeks is to be recorded. (a) List the sample space. (b) If a different type of soft drink is purchased than in the previous
> Calculate the mean and standard deviation of the binomial distribution using the formulas in mean = n p (a) If n is changed to 20. (b) When n 20. (c) When n = 40.
> 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
> About 30% of adults say that reading is a favorite leisure activity. Let success be the outcome that reading is a favorite leisure activity. Find the probability that: (a) More than 5 trials are needed in order to obtain 3 successes. (b) More than 9 tri
> 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
> 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
> A market researcher intends to study the consumer preference between regular and decaffeinated coffee. Examine the plausibility of the model of Bernoulli trials in the following situations. (a) One hundred consumers are randomly selected and each is ask
> 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
> From four agricultural plots, two are selected at random for a pesticide treatment. The other two plots serve as controls. For each plot, denote by S the event that it is treated with the pesticide. Consider the assignment of treatment or control to a si
> Refer to Exercise 5.43 but instead assume that the jar contains 2000 pieces of wrapped hard candies, of which 700 are raspberry, 1000 are butterscotch , and 300 are other flavors. Repeat parts (a)-(c) of Exercise 5.43 in this setting. Data from Exercise
> A jar contains 20 pieces of wrapped hard candies, 7 are raspberry, 10 are butterscotch, and 3 are other flavors. Consider 4 successive draws of 1 piece of candy taken at random from the jar. Suppose the selection of butterscotch is the event of interest.
> In each case, examine whether or not repetitions of the stated experiment conform to the model of Bernoulli trials. Where the model is appropriate, determine the numerical value of p or indicate how it can be determined. (a) Roll a fair die and observe
> Is the model of Bernoulli trials plausible in each of the following situations? Discuss in what manner (if any) a serious violation of the assumptions can occur. (a) Seven friends go to a blockbuster movie and each is asked whether the movie was excellen
> Given the two probability distributions (a) Construct probability histograms. Which distribution has a larger spread? (b) Verify that both distributions have the same mean. (c) Compare the two standard deviations.
> Definition: The median of a distribution is the value m0 of the random variable such that P [X ≤ m0] ≥ .5 and P [X ≥ m0] ≥ .5 . In other words, the probability at or below m0 is at le
> Given here are the probability distributions of two random variables X and Y. (a) From the X distribution, determine the distribution of the random variable 8 - 2X and verify that it coincides with the Y distribution. (b) Calculate the mean and standard
> Determine a 99% confidence interval for µ using the data in Exercise 9.49. Data from Exercise 9.49: Measurements of the amount of suspended solids in river water on 14 Monday mornings yield x = 47 and s = 9 .4 mg/I. Obtain a 95% confidence interval for
> Measurements of the amount of suspended solids in river water on 14 Monday mornings yield x = 47 and s = 9 .4 mg/I. Obtain a 95% confidence interval for the mean amount of suspended solids. State any assumption you make about the population.
> A t distribution assigns more probability to large values than the standard normal. (a) Find t.05 for d.f = 12 and then evaluate P [ Z > t.05 ] . Verify that P [ T > t.05 ] is greater than P [Z > t.05] . (b) Examine the relation for d.f of 5 and 20, and
> Using software or the table of percentage points for the t distributions, find (a) t.05 when d.f = 7. (b) t.025 when d.f = 11. (c) The lower .05 point when d.f = 7. (d) The lower .05 point when d.f = 11.
> Refer to participants wore a counting device for a week, and each day they counted the number of times they thought about food. The average of the seven counts is intended to represent a typical day. For 19 males, we have times per day. (a) Make a graphi
> Refer to the computer anxiety scores (CARS) for males in the Data Bank. Conduct an a = .025 level of H0 : µ = 2.7 versus H1 : µ > 2.7.
> Refer to the data on the length (cm) of m ale grizzly bears given in the Data Bank. (a) Find a 99% confidence interval for the population mean. (b) Is the population mean length for all m ale grizzly b ears in Alaska contained in this interval? (c) Ex
> Refer to the computer output concerning the head length (cm) of male grizzly bears in Exercise 9.68. (a) Is the population mean head length for all m ale bears in the study area contained in this interval ? (b) Explain why you are 95% confident that it
> The probability distribution of a random variable X is given by the function (a) Calculate the numerical probabilities and list the distribution. (b) Calculate the mean and standard deviation of X.
> Refer to the data on the head length (cm) of male grizzly bears given in the Data Bank. A computer calculation for a test of H0 : µ = 21 versus H1 : µ ≠21 is given below. (a) What is the conclusion if you test
> Refer to the water quality data. Perform a test of hypotheses with the intent of showing that the population standard deviation is less than 18.0. Take a = .05.
> Refer to the data of Exercise 9.60. Is there strong evidence that the standard deviation for the efficiency of the new model is below 3.0? Data from Exercise 9.60: Combustion efficiency measurements were recorded for 10 home heating furnaces of a new mo
> Conduct a test of hypothesis with the intent of establishing that the mean bottle life is different from 55 .0 days. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c) Give the form of the rejection region. (d) W
> Use software to find (a) The 90th percentile of x2 wh en d.f = 13. (b) The 10th percentile of x2 when d.f = 4. (c) The median of x2 when d.f = 32. (d) The 1st percentile of x2 when d.f. = 46.
> Use software to find (a) x2.05 with d.f = 3 . (b) x2.025 with d .f = 24. (c) The lower .05 point with d.f = 7. (d) The lower .025 point with d .f. = 32.
> Times to finish a sixteen ounce bottle of mayonnaise, were recorded by a sample of 11 purchasers. It is determined that Σxi = 645.7 days and Σ(xi - x)2 = 198.41. (a) Obtain a point estimate of the population mean life µ and its 90% error margin . (b) Ob
> A person with asthma took measurements by blowing into a peak-flow meter on seven consecutive days. / (a) Obtain a 95% confidence interval for the population mean peak-flow. (b) Conduct an a = .10 level test of H0 : µ = 453 versus H1 : µ ≠ 453.
> Combustion efficiency measurements were recorded for 10 home heating furnaces of a new model. The sample mean and standard deviation were found to be 73.2 and 2.74, respectively. Do these results provide strong evidence that the average efficiency of the
> A car advertisement asserts that with the new collapsible bumper system, the average body repair cost for the damages sustained in a collision impact of 10 miles per hour does not exceed $1500. To test the validity of this claim, 5 cars are crashed into
> Suppose the probability distribution of a random variable X has the distribution f( X) = 60/77 1/x for x = 2, 3, 4, 5 Calculate the mean and standard deviation of this distribution.
> The supplier of a particular brand of vitamin pills claims that the average potency of these pills after a certain exposure to heat and humidity is at least 65. Before buying these pills, a distributor wants to verify the supplier's claim is valid. To th
> Refer to concerning the yield of green gasoline. Conduct a test of hypothesis which is intended to show that the mean product volume is greater than 2. 7 5 liters. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c
> Referring to Exercise 9 .55, test H0 : µ = 2.8 versus H1 : µ ≠2.8 using a = .02. Data from Exercise 9.55: In a study of head injuries to ice hockey players the number of hits were monitored electronically by
> In a study of head injuries to ice hockey players the number of hits were monitored electronically by equipping approved helmets with accelerometers that measured head acceleration (m/s2) when a player was hit. The researchers counted the number of serio
> Refer to the data on the heights of red pine seedlings in Exercise 8.3. Use MINITAB to: (a) Find a 97% percent confidence interval for the mean height. (b) Test H0 : µ = 1.9 versus H1 : µ ≠1.9 centimeters wi
> Refer to the data on percent malt extract in the Data Bank. A computer summary of a level a = .05 test of H0 : µ = 77 versus a two-sided alternative and a 95% confidence interval is given below: (a) Will the 98% confidence interval for mean
> Refer to the data on the computer attitude score (CAS) in the Data Bank. A computer summary of a level a = .05 test of H0 : µ = 2.6 versus a two-sided alternative and a 95% confidence interval is given below. (a) Will the 99% confidence inte
> Consider the problem of testing H0: µ = 10 versus H1 :µ > 10 with n = 64, u = 2 (known), and a = .025 . The rejection region of this test is given by Suppose we wish to calculate the power of this test at the alternative &Aci
> Refer to Exercise 8.2 where participants wore a counting device for a week, and each day they counted the number of times they thought about food. The average of the seven daily counts, for each of n = 65 participants, are summarized by the statistics n
> A genetic model suggests that 80% of the plants grown from a cross between two given strains of seeds will be of the dwarf variety. After breeding 200 of these plants, 136 were observed to be of the dwarf variety. (a) Does this observation strongly cont
> Upon examination of the claims records of 280 policy holders over a period of five years, an insurance company makes an empirical determination of the probability distribution of X = number of claims in five years. (a) Calculate the expected value of X.
> Each year, an insurance company reviews its claim experience in order to set future rates. Regarding their damage-only automobile insurance policies, at least one claim was made on 2073 of the 12,299 policies in effect for the year. Treat these data as a
> In one 45-day period, American Airlines flew 152 flights from Chicago, Illinois, to Austin, Texas. Of these, 22 arrived late. Treat this as a random sample and conduct a test with the intent of establishing that the population proportion of late flights
> With reference to Exercise 8.90, conduct a test with the intent of establishing that p > .20. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c) Give the form of the rejection region. (d) What is the conclusion t
> Out of a sample of n = 625 students interviewed, 139 had missed at least one class last week. Obtain a 95% confidence interval for p = proportion of all students that missed at least one class last week.
> With reference to Exercise 8.88, (a) Conduct a test of size .OS with the intent of establishing that the proportion today is larger than .67. (b) Find a 95% confidence interval for that proportion. Data from Exercise 8.88: In a recent year, 67% of per
> In a recent year, 67% of persons 22-33 years old held passports. From a random sample of size n = 79 collected today, 61 are passport holders. (a) Estimate the proportion of persons 22-33 years old who hold passports today. (b) Estimate a 95% error mar
> The daily number of kayaks sold, X, at a water sports store has the probability distribution (a) Find the expected number of kayaks sold in a day. (b) Find the standard deviation of the number of kayaks sold in a day. (c) Suppose data from the next 64
> After feeding a special diet to 80 mice, the scientist measures their weight in grams and obtains x = 35 grams and s = 4 grams. He states that a 90% confidence interval for µ is given by (a) Was the confidence interval calculated correctly?
