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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+e. To the right of 25f. Between 21.6 and 2.5 g. To the left of 0.23
=+7.17 Determine each of the areas under the standard normal (z) curvea. To the left of 21.28b. To the right of 1.28c. Between 21 and 2d. To the right of 0
=+f. The area under the z curve between 21 and 1 g. The area under the z curve between 24 and 4
=+a. The area under the z curve to the left of 1.75b. The area under the z curve to the left of 20.68c. The area under the z curve to the right of 1.20d. The area under the z curve to the right of 22.82e. The area under the z curve between 22.22 and 0.53
=+7.16 Determine the following standard normal (z) curve areas:
=+c. What is the probability that reaction time is at most 0.25 sec?
=+b. What is the probability that reaction time exceeds 0.5 sec?
=+a. What is the height of the density curve above x 5 0? (Hint: Total area 5 1.)
=+7.15 Let x denote the time (in seconds) necessary for an individual to react to a certain stimulus. The probability distribution of x is specified by the following density curve:
=+c. What is the probability that a randomly selected package of this type weighs at least 0.75 lb?
=+b. What is the probability that a randomly selected package of this type weighs between 0.25 lb and 0.5 lb?
=+a. What is the probability that a randomly selected package of this type weighs at most 0.5 lb?
=+7.14 A delivery service charges a special rate for any package that weighs less than 1 lb. Let x denote the weight of a randomly selected parcel that qualifies for this special rate. The probability distribution of x is specified by the following density curve:Use the fact that the area of a
=+d. Because the density curve is symmetric, the mean of the distribution is .20. What is the probability that thickness is within 0.05 mm of the mean thickness?Density 0 0.20 Thickness 50.40 110 0 10 Time(minutes)Density x
=+c. What is the probability that x is between .10 and .20?(Hint: First find the probability that x is not between .10 and .20.)
=+b. What is the probability that x is less than .20? less than.10? more than .30?
=+a. Verify that the total area under the density curve is equal to 1. (Hint: The area of a triangle is equal to 0.5(base)(height).)
=+7.13 Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the variable x 5 thickness (in millimeters). Suppose that a reasonable model for the population distribution is the one shown in the following figure:
=+c. What do you think is the value of the mean of this distribution?
=+b. What is the probability that between 3 and 5 min elapse before dismissal?
=+a. What is the probability that at most 5 min elapse before dismissal?
=+vthat elapses before the professor dismisses class. Suppose that the density curve shown in the following figure is an appropriate model for the probability distribution of x:
=+7.12 A particular professor never dismisses class early.0 25 50 Let x denote the amount of time past the hour (in minutes)
=+d. The probability that the lifetime is at least 25 hre. The probability that the lifetime exceeds 30 hr
=+7.11 Consider the population of batteries made by a particular manufacturer. The following density curve represents the probability distribution for the variable x 5 lifetime (in hours):Shade the region under the curve corresponding to each of the following probabilities (draw a new curve for
=+7.10 A certain basketball player makes 70% of his free throws. Assume that results of successive free throws are independent of one another. At the end of a particular practice, the coach tells the player to begin shooting free throws and to stop only when he has made two consecutive shots. Let
=+e. One of the two distributions pictured has a standard deviation of approximately 100, and the other has a standard deviation of about 175. What is the standard deviation of the distribution for the variable x (lifetime for a bulb made by Supplier 1)?
=+d. One of the two distributions pictured has a mean of approximately 1000, and the other has a mean of about 900. What is the mean of the distribution for the variable x(lifetime for a bulb made by Supplier 1)?
=+c. Assuming that the cost of the light bulbs is the same for both suppliers, which supplier would you recommend?Explain.
=+b. Which population distribution has the larger standard deviation?
=+a. Which population distribution has the larger mean?
=+Five hundred bulbs from each supplier are tested, and the lifetime of each bulb is recorded. The density histograms above are constructed from these two sets of observations.Although these histograms are constructed using data from only 500 bulbs, they can be considered approximations to the
=+7.9 A company receives light bulbs from two different suppliers. Define the variables x and y by x 5 lifetime of a bulb from Supplier 1 y 5 lifetime of a bulb from Supplier 2
=+c. Use the population distribution to determine the following probabilities.i. P(x $ 15) ii. P(x , 9) iii. P(12 # x , 18)
=+b. Is the population distribution symmetric or skewed?
=+a. Calculate the relative frequency and density for each of the seven intervals in the frequency distribution. Use the computed densities to construct a density histogram for the variable x 5 homicide rate for the population consisting of the 50 states.
=+7.8 Homicide rate (homicides per 100,000 population) for each of the 50 states appeared in the San Luis Obispo Telegram-Tribune (February 2, 1995). A frequency distribution constructed from the 50 observations is shown in the following table:Homicide Rate Frequency 0 to ,3 5 3 to ,6 16 6 to ,9 9
=+c. If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight? What if you are number 3?
=+b. What is the probability that not all passengers can be accommodated?
=+a. What is the probability that the airline can accommodate everyone who shows up for the flight?
=+7.1 ■ Describing the Distribution of Values in a Population 303 Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the population distribution of x is given in the following table:x Proportion x Proportion 95 .05 103 .03 96 .10 104
=+7.7 Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations.
=+d. It can be shown that the mean value of x is approximately 14.8 in. What is the approximate probability that x is within 2 in. of this mean value?
=+c. Approximate P(x # 16).
=+b. Approximate P(x , 16).
=+a. Construct a relative frequency histogram to represent the approximate distribution of this variable.
=+7.6 A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza gave the following proportions for the various sizes:Size 12 in. 14 in. 16 in. 18 in.Proportion .20 .25 .50 .05 With x denoting the size of a pizza in a single-pizza order, the given table is an
=+Three attempts were made to contact each graduate; a donation of $0 was recorded both for those who were contacted but who declined to make a donation and for those who were not reached in three attempts. Consider the variable x 5 amount of donation for the population of last year’s
=+7.5 Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates:Size of donation $0 $10 $25 $50 Proportion of calls .45 .30 .20 .05
=+b. Based on the given information, we can write P(x 5 false alarm) 5 .25. Use the other two relative frequencies shown in the bar chart from Part (a) to write two other probability statements.
=+a. Construct a relative frequency bar chart that represents the distribution of the variable x 5 type of call, where type of call has three categories: false alarm, small fire, and major fire. What is the underlying population for this variable?
=+7.4 Based on past history, a fire station reports that 25%of the calls to the station are false alarms, 60% are for small fires that can be handled by station personnel without outside assistance, and 15% are for major fires that require outside help.
=+b. If an individual is randomly selected from this population, what is the probability that the selected homeowner does not have earthquake insurance?
=+a. Construct a relative frequency bar chart that represents the population distribution for x for the case where 60% of the county homeowners have earthquake insurance.
=+7.3 Consider the variable x 5 earthquake insurance status for the population of homeowners in an earthquake-prone California county. This variable associates a category (insured or not insured) with each individual in the population.
=+g. The number of traffic citations issued by the highway patrol in a particular county on a given day
=+e. The tension (in pounds per square inch) at which a tennis racket is strungf. The amount of water used by a household during a given month
=+b. The amount of rainfall at a particular location during the next yearc. The distance that a person throws a baseballd. The number of questions asked during a 1-hr lecture
=+a. The fuel efficiency (in miles per gallon) of an automobile
=+7.2 Classify each of the following numerical variables as either discrete or continuous:
=+c. The number of pages in a bookd. The number of checkout lines operating at a large grocery storee. The lifetime of a light bulb
=+7.1 State whether each of the following numerical variables is discrete or continuous:a. The number of defective tires on a carb. The body temperature of a hospital patient
=+g. Why do the estimated probabilities from Parts (e) and(f) differ? Which do you think is a better estimate of the true probability? Explain.
=+f. Ask four classmates for their simulation results. Along with your own results, this should give you information on 50 simulated tournaments. Use this information to estimate the probability that the first seed wins the tournament.
=+e. Simulate 10 tournaments, and use the resulting information to estimate the probability that the first seed wins the tournament.
=+d. Simulate one complete tournament, giving an explanation for each step in the process.
=+c. How would you use a selection of random digits to simulate the third game in the tournament? (This will depend on the outcomes of Games 1 and 2.)
=+b. Describe how you would use a selection of random digits to simulate Game 2 of this tournament.
=+a. Describe how you would use a selection of random digits to simulate Game 1 of this tournament.
=+2, the players seeded second and third play. In Game 3, the winners of Games 1 and 2 play, with the winner of Game 3 declared the tournament winner. Suppose that the following probabilities are given:P(Seed 1 defeats Seed 4) 5 .8 P(Seed 1 defeats Seed 2) 5 .6 P(Seed 1 defeats Seed 3) 5 .7 P(Seed
=+6.34 A single-elimination tournament with four players is to be held. A total of three games will be played. In Game 1, the players seeded (rated) first and fourth play. In Game
=+d. If neither player earns any points from a draw, would the simulation requested in Part (c) take longer to perform? Explain your reasoning.
=+c. If a draw earns a half-point for each player, describe how you would perform a simulation experiment to estimate P(A wins the championship).
=+b. What is the probability that it takes just five games to obtain a champion?
=+a. What is the probability that A wins the championship in just five games?
=+5 .2, and P(draw) 5 .5. Each time a player wins a game, he earns one point and his opponent earns no points. The first player to win 5 points wins the championship. For the sake of simplicity, assume that the championship will end in a draw if both players obtain 5 points at the same time.
=+6.33 Two individuals, A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw.Suppose that the outcomes of successive games are independent, with P(A wins game) 5 .3, P(B wins game)
=+Use this information to approximate the probability that a randomly selected pregnant woman who reaches full terma. Delivers twinsb. Delivers quadrupletsc. Gives birth to more than a single child
=+6.32 Suppose that the following information on births in the United States over a given period of time is available to you:Type of Birth Number of Births Single birth 41,500,000 Twins 500,000 Triplets 5,000 Quadruplets 100
=+is the probability that the request is for a composer who wrote at least one symphony?
=+c. Neither Bach nor Wagner wrote any symphonies. What
=+b. What is the probability that the request is not for one of the two S’s?
=+a. What is the probability that the request is for one of the three B’s?
=+6.31 A radio station that plays classical music has a “by request” program each Saturday evening. The percentages of requests for composers on a particular night are as follows:Bach 5%Mozart 21%Beethoven 26%Schubert 12%Brahms 9%Schumann 7%Dvorak 2%Tchaikovsky 14%Mendelssohn 3%Wagner 1%Suppose
=+c. What is the probability that the size purchased is larger than a pint?
=+b. What is the probability that Von’s brand is not purchased?
=+a. What is the probability that Dreyer’s ice cream is purchased?
=+6.30 Consider the five outcomes (shown in the table on page 293) for an experiment in which the type of ice cream purchased by the next customer at a certain store is noted.
=+d. Calculation of the probability in Part (c) required that we assume independence of Outcomes 1 and 2. If the outcomes are independent, knowing that one team had 10 or more hits would not change the probability that the other team had 10 or more hits. Do you think that the independence
=+c. Assume that the following outcomes are independent:Outcome 1: Home team got 10 or more hits.Outcome 2: Visiting team got 10 or more hits.What is the probability that both teams got 10 or more hits?
=+b. What is the probability that the home team got more than 13 hits?
=+a. If one of these games is selected at random, what is the probability that the visiting team got fewer than 3 hits?
=+6.29 The article “Baseball: Pitching No-Hitters” (Chance[summer 1994]: 24–30) gives information on the number of hits per team per game for all nine-inning major league games played between 1989 and 1993. Each game resulted in two observations, one for each team. No distinction was made
=+e. Answer the question posed in Part (d) if only 4200 of the students have both cards.
=+d. Are the outcomes has a Visa card and has a MasterCard independent? Explain.
=+c. Suppose that you learn that the selected individual has a Visa card (was one of the 7000 with such a card). Now what is the probability that this student has both cards?
=+b. What is the probability that the selected student has both cards?
=+a. What is the probability that the selected student has a Visa card?
=+6.28 Of the 10,000 students at a certain university, 7000 have Visa cards, 6000 have MasterCards, and 5000 have both. Suppose that a student is randomly selected.
=+7. Do you think that the assumption that the outcomes of successive free throws are independent is reasonable?Explain. (This is a hotly debated topic among both sports fans and statisticians!)
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