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Introductory Statistics 8th Edition Prem S. Mann - Solutions

Find the area under the standard normal curve a. To the right of z = 1.36 b. To the left of z = –1.97 c. To the right of z = –2.05 d. To the left of z = 1.76
Obtain the area under the standard normal curve a. To the right of z = 1.43 b. To the left of z = –1.65 c. To the right of z = –.65 d. To the left of z = .89
Find the area under the standard normal curve a. Between z = 0 and z = 4.28 b. From z = 0 to z = –3.75 c. To the right of z = 7.43 d. To the left of z = –4.69
Find the area under the standard normal curve a. From z = 0 to z = 3.94 b. Between z = 0 and z = –5.16 c. To the right of z = 5.42 d. To the left of z = –3.68
Determine the following probabilities for the standard normal distribution. a. P(–1.83 < z < 2.57) b. P(0 < z < 2.02) c. P(–1.99 < z < 0) d. P(z > 1.48)
Determine the following probabilities for the standard normal distribution. a. P(–2.46 < z < 1.88) b. P(0 < z < 1.96) c. P(–2.58 < z < 0) d. P(z > .73)
Find the following probabilities for the standard normal distribution. a. P(z < –2.34) b. P(.67 < z < 2.59) c. P(–2.07 < z < –.93) d. P(z < 1.78)
Find the following probabilities for the standard normal distribution. a. P(z < –1.31) b. P(1.23 < z < 2.89) c. P(–2.24 < z < –1.19) d. P(z < 2.02)
Obtain the following probabilities for the standard normal distribution. a. P(z > –.98) b. P(–2.47 < z < 1.29) c. P(0 < z < 4.25) d. P(–5.36 < z < 0) e. P(z > 6.07) f. P(z < –5.27)
Obtain the following probabilities for the standard normal distribution. a. P(z > –1.86) b. P(–.68 < z < 1.94) c. P(0 < z < 3.85) d. P(–4.34 < z < 0) e. P(z > 4.82) f. P(z < –6.12)
Find the z value for each of the following x values for a normal distribution with µ = 30 and σ = 5.a. x = 39b. x = 19c. x = 24d. x = 44
Determine the z value for each of the following x values for a normal distribution with µ = 16 and µ = 3. a. x = 12 b. x = 22 c. x = 19 d. x = 13
Find the following areas under a normal distribution curve with µ = 20 and µ = 4. a. Area between x = 20 and x = 27 b. Area from x = 23 to x = 26 c. Area between x = 9.5 and x = 17
For a continuous probability distribution, explain why the following holds true.
Find the following areas under a normal distribution curve with µ = 12 and µ = 2. a. Area between x = 7.76 and x = 12 b. Area between x = 14.48 and x = 16.54 c. Area from x = 8.22 to x = 10.06
Determine the area under a normal distribution curve with µ = 55 and µ = 7 a. To the right of x = 58 b. To the right of x = 43 c. To the left of x = 68 d. To the left of x = 22
Find the area under a normal distribution curve with µ = 18.3 and µ = 3.4 a. To the left of x = 10.9 b. To the right of x = 14 c. To the left of x = 22.7 d. To the right of x = 29.2
Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35
Let x be a continuous random variable that has a normal distribution with a mean of 117.6 and a standard deviation of 14.6. Find the probability that x assumes a value a. Between 77.9 and 98.3 b. Between 85.3 and 142.6
Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. Greater than 69 b. Less than 73 c. Greater than 101 d. Less than 87
Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value a. Less than 45 b. Greater than 79 c. Greater than 54 d. Less than 70
Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. In less than 160
According to the U.S. Employment and Training Administration, the average weekly unemployment benefit paid out in 2008 was $297 (www.ows.doleta.gov/unemploy/hb394.asp). Suppose that the current distribution of weekly unemployment benefits paid out is approximately normally distributed with a mean
According to the National Retail Federation’s recent Back to College Consumer Intentions and Actions survey, families of college students spend an average of $616.13 on new apparel, furniture for dorms or apartments, school supplies, and electronics
Briefly explain the main characteristics of a normal distribution. Illustrate with the help of graphs.
Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his times between pitches are normally distributed with a mean of 36 seconds and a standard deviation of 2.5 seconds. What percentages of his times between pitches are a.
A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a standard deviation of 4 miles per hour. Find the percentage of vehicles passing through this
The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of $845 and a standard deviation of $270. Assume that the balances on all these Visa cards follow a normal distribution. a. What
A 2011 analysis performed by Read Write Mobile revealed that the average number of apps downloaded per day per iOS device (such as iPhone, iPod, and iPad) exceeds 60 (www.readwriteweb.com/ mobile/2011/01/more-than-60-apps-downloaded-per-ios-device.php). Suppose that the current distribution of apps
The transmission on a model of a specific car has a warranty for 40,000 miles. It is known that the life of such a transmission has a normal distribution with a mean of 72,000 miles and a standard deviation of 13,000 miles. a. What percentage of the transmissions will fail before the end of the
According to the records of an electric company serving the Boston area, the mean electricity consumption for all households during winter is 1650 kilowatt-hours per month. Assume that the monthly electricity consumptions during winter by all households in this area have a normal distribution with
The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all
One of the cars sold by Walt’s car dealership is a very popular subcompact car called Rhino. The final sale price of the basic model of this car varies from customer to customer depending on the negotiating skills and persistence of the customer. Assume that these sale prices of this car are
A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10) for patients waiting for root canal treatments are found to be approximately normally distributed with a mean of 7.59 and a standard deviation
According to the U.S. Department of Agriculture, the average American consumed 54.3 pounds (approximately seven gallons) of salad and cooking oils in 2008 (www.ers.usda.gov/data/foodconsumption). Suppose that the current distribution of salad and cooking oil consumption is approximately normally
Briefly describe the standard normal distribution curve.
Fast Auto Service guarantees that the maximum waiting time for its customers is 20 minutes for oil and lube service on their cars. It also guarantees that any customer who has to wait longer than 20 minutes for this service will receive a 50% discount on the charges. It is estimated that the mean
The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviation of .009 inch. The nails that are either shorter than 2.98 inches or longer than 3.02 inches are unusable. What percentage of all the nails produced by this machine are
The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.75 ounces and a standard deviation of .11 ounce. What percentage of the pucks produced at this factory
Find the value of z so that the area under the standard normal curve a. From 0 to z is .4772 and z is positive b. Between 0 and z is (approximately) .4785 and z is negative c. In the left tail is (approximately) .3565 d. In the right tail is (approximately) .1530
Find the value of z so that the area under the standard normal curve a. From 0 to z is (approximately) .1965 and z is positive b. Between 0 and z is (approximately) .2740 and z is negative c. In the left tail is (approximately) .2050 d. In the right tail is (approximately) .1053
Determine the value of z so that the area under the standard normal curve a. In the right tail is .0500 b. In the left tail is .0250 c. In the left tail is .0100 d. In the right tail is .0050
Determine the value of z so that the area under the standard normal curve a. In the right tail is .0250 b. In the left tail is .0500 c. In the left tail is .0010 d. In the right tail is .0100
Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25. a. Find the value of x so that the area under the normal curve to the left of x is approximately .6330. b. Find the value of x so that the area under the normal curve to the
Let x be a continuous random variable that follows a normal distribution with a mean of 550 and a standard deviation of 75. a. Find the value of x so that the area under the normal curve to the left of x is .0250. b. Find the value of x so that the area under the normal curve to the right of x is
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its
The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all
According to the records of an electric company serving the Boston area, the mean electricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a
Rockingham Corporation makes electric shavers. The life (period during which a shaver does not need a major repair) of Model J795 of an electric shaver manufactured by this corporation has a normal distribution with a mean of 70 months and a standard deviation of 8 months. The company is to
A study has shown that 20% of all college textbooks have a price of $184.52 or higher. It is known that the standard deviation of the prices of all college textbooks is $36.35. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?
A machine at Keats Corporation fills 64-ounce detergent jugs. The machine can be adjusted to pour, on average, any amount of detergent into these jugs. However, the machine does not pour exactly the same amount of detergent into each jug; it varies from jug to jug. It is known that the net amount
For a binomial probability distribution, n = 20 and p = .60.a. Find the probability P(x 14) by using the table of binomial probabilities (Table I of Appendix C).b. Find the probability P(x = 14) by using the normal distribution as an approximation to the binomial distribution. What is the
For a binomial probability distribution, n = 25 and p = .40.a. Find the probability P(8 < x < 13) by using the table of binomial probabilities (Table I of Appendix C).b. Find the probability P(8 < x < 13) by using the normal distribution as an approximation to the binomial distribution.
For a binomial probability distribution, n = 80 and p = .50. Let x be the number of successes in 80 trials.a. Find the mean and standard deviation of this binomial distribution.b. Find P(x > 42) using the normal approximation.c. Find P(41 < x < 48) using the normal approximation.
For a binomial probability distribution, n = 120 and p = .60. Let x be the number of successes in 120 trials.a. Find the mean and standard deviation of this binomial distribution.b. Find P(x < 69) using the normal approximation.c. Find P(67 < x < 73) using the normal approximation.
Find the following binomial probabilities using the normal approximation.a. n = 140, p = .45, P(x = 67)b. n = 100, p = .55, P(52 < x < 60)c. n = 90, p = .42, P(x > 40)d. n = 104, p = .75, P(x < 72)
Find the following binomial probabilities using the normal approximation.a. n = 70, p = .30, P(x = 18)b. n = 200, p = .70, P(133 < x < 145)c. n = 85, p = .40, P(x > 30)d. n = 150, p = .38, P(x < 62)
According to the U.S. Census American Community Survey, 5.44% of workers in Portland, Oregon, commute to work on their bicycles. Find the probability that in a sample of 400 workers from Portland, Oregon, the number who commute to work on their bicycles is 23 to 27.
According to an Allstate/National Journal poll, 39% of the U.S. adults polled said that it is extremely or very likely that “there will be a female president within 10–15 years” in the United States (USA Today, March 28, 2012). Suppose that this percentage is true for the current population
The percentage of women in the work force has increased tremendously during the past few decades. Whereas only 35% of all employees in the United States in 1970 were women, this percentage is now 49% (Bloomberg Business week, January 9–January 15, 2012). Suppose that currently 49% of all
According to a November 8, 2010 report on www.teleread.com, 7% of U.S. adults with online services currently read e-books. Assume that this percentage is true for the current population of U.S. adults with online services. Find the probability that in a random sample of 600 U.S. adults with online
According to a Gallup poll, 92% of Americans believe in God (Time, June 20, 2011). Suppose that this result is true for the current population of adult Americans. What is the probability that the number of adult Americans in a sample of 500 who believe in God isa. Exactly 445b. At least 450c. 440
An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of the people who tried the shredder were satisfied with it. Because of this high satisfaction rate, the company decided to market the new shredder. Assume that 80% of all
Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees the refund of money or a replacement for any calculator that malfunctions within two years from the date of purchase. It is known from past data that
Hurbert Corporation makes font cartridges for laser printers that it sells to Alpha Electronics Inc.The cartridges are shipped to Alpha Electronics in large volumes. The quality control department at Alpha Electronics randomly selects 100 cartridges from each shipment and inspects them for being
The management at Ohio National Bank does not want its customers to wait in line for service for too long. The manager of a branch of this bank estimated that the customers currently have to wait an average of 8 minutes for service. Assume that the waiting times for all customers at this branch
A company that has a large number of supermarket grocery stores claims that customers who pay by personal checks spend an average of $87 on groceries at these stores with a standard deviation of $22. Assume that the expenses incurred on groceries by all such customers at these stores are normally
At Jen and Perry Ice Cream Company, the machine that fills 1-pound cartons of Top Flavor ice cream is set to dispense 16 ounces of ice cream into every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in
A machine at Kasem Steel Corporation makes iron rods that are supposed to be 50 inches long. However, the machine does not make all rods of exactly the same length. It is known that the probability distribution of the lengths of rods made on this machine is normal with a mean of 50 inches and a
Jenn Bard, who lives in the San Francisco Bay area, commutes by car from home to work. She knows that it takes her an average of 28 minutes for this commute in the morning. However, due to the variability in the traffic situation every morning, the standard deviation of these commutes is 5 minutes.
The print on the package of Sylvania CFL 65W replacement bulbs that use only 16W claims that these bulbs have an average life of 8000 hours. Assume that the distribution of lives of all such bulbs is normal with a mean of 8000 hours and a standard deviation of 400 hours. Let x be the life of a
Major League Baseball rules require that the balls used in baseball games must have circumferences between 9 and 9.25 inches. Suppose the balls produced by the factory that supplies balls to Major League Baseball have circumferences normally distributed with a mean of 9.125 inches and a standard
According to an article on Yahoo.com on February 19, 2012, the average salary of actuaries in the U.S. is $98,620 a year (education.yahoo.net/articles/careers_for_shy_people_2.htm?kid=1KWO3). Suppose that currently the distribution of annual salaries of all actuaries in the U.S. is approximately
Mong Corporation makes auto batteries. The company claims that 80% of its LL70 batteries are good for 70 months or longer.a. What is the probability that in a sample of 100 such batteries, exactly 85 will be good for 70 months or longer?b. Find the probability that in a sample of 100 such
Stress on the job is a major concern of a large number of people who go into managerial positions. It is estimated that 80% of the managers of all companies suffer from job-related stress.a. What is the probability that in a sample of 200 managers of companies, exactly 150 suffer from job-related
For the standard normal distribution, what does z represent?
It is known that 15% of all homeowners pay a monthly mortgage of more than $2500 and that the standard deviation of the monthly mortgage payments of all homeowners is $350. Suppose that the monthly mortgage payments of all homeowners have a normal distribution. What is the mean monthly mortgage
At Jen and Perry Ice Cream Company, a machine fills 1-pound cartons of Top Flavor ice cream. The machine can be set to dispense, on average, any amount of ice cream into these cartons. However, the machine does not put exactly the same amount of ice cream into each carton; it varies from carton to
Two companies, A and B, drill wells in a rural area. Company A charges a flat fee of $3500 to drill a well regardless of its depth. Company B charges $1000 plus $12 per foot to drill a well. The depths of wells drilled in this area have a normal distribution with a mean of 250 feet and a standard
Otto is trying out for the javelin throw to compete in the Olympics. The lengths of his javelin throws are normally distributed with a mean of 253 feet and a standard deviation of 8.4 feet. What is the probability that the longest of three of his throws is 270 feet or more?
Lori just bought a new set of four tires for her car. The life of each tire is normally distributed with a mean of 45,000 miles and a standard deviation of 2000 miles. Find the probability that all four tires will last for at least 46,000 miles. Assume that the life of each of these tires is
The Jen and Perry Ice Cream company makes a gourmet ice cream. Although the law allows ice cream to contain up to 50% air, this product is designed to contain only 20% air. Because of variability inherent in the manufacturing process, management is satisfied if each pint contains between 18% and
The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at 1-mile intervals.
Ashley knows that the time it takes her to commute to work is approximately normally distributed with a mean of 45 minutes and a standard deviation of 3 minutes. What time must she leave home in the morning so that she is 95% sure of arriving at work by 9 A.M.?
A soft-drink vending machine is supposed to pour 8 ounces of the drink into a paper cup. However, the actual amount poured into a cup varies. The amount poured into a cup follows a normal distribution with a mean that can be set to any desired amount by adjusting the machine. The standard deviation
According to the College Board (professionals.collegeboard.com/gateway), the mean SAT mathematics score for all college-bound seniors was 511 in 2011. Suppose that this is true for the current population of college-bound seniors. Furthermore, assume that 17% of college-bound seniors scored below
1. The normal probability distribution is applied to a. A continuous random variable b. A discrete random variable c. Any random variable 2. For a continuous random variable, the probability of a single value of x is always a. Zero b. 1.0 c. Between 0 and 1 3. Which of the following is not a
Find the value of z for the standard normal curve such that the area a. In the left tail is .1000 b. Between 0 and z is .2291 and z is positive c. In the right tail is .0500 d. Between 0 and z is .3571 and z is negative
In a National Highway Traffic Safety Administration (NHTSA) report, data provided to the NHTSA by Goodyear stated that the average tread life of properly inflated automobile tires is 45,000 miles. Suppose that the current distribution of tread life of properly inflated automobile tires is normally
Refer to Problem 11. a. Suppose that 6% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x. b. Suppose that 2% of all automobile tires with the shortest tread life have a tread life of at most x miles. Find the value of x. In Exercise
Gluten sensitivity, which is also known as wheat intolerance, affects approximately 15% of people. The condition involves great difficulty in digesting wheat, but is not the same as wheat allergy, which has much more severe reactions .A random sample of 800 individuals is selected. a. Find the
Find the following probabilities for the standard normal distribution. a. P(.85 < z < 2.33) b. P(–2.97 < z < 1.49) c. P(z < –1.29) d. P(z > –.74)
Briefly explain the meaning of a population distribution and a sampling distribution. Give an example of each.
What is an estimator? When is an estimator unbiased? Is the sample mean, , an unbiased estimator of µ? Explain.
According to a Time Magazine/ABT SRBI poll conducted by telephone during October 9–10, 2011, 73% of adult’s age 18 years and older said that they are in favor of raising taxes on those with annual incomes of $1 million or more to help cut the federal deficit (Time, October 24, 2011). Assume
Refer to Exercise 7.100. Assume that 73% of adults age 18 years and older are in favor of raising taxes on those with annual incomes of $1 million or more to help cut the federal deficit. A random sample of 900 American adults age 18 years and older is selected. a. Find the probability that the
According to a Pew Research Center nationwide telephone survey of American adults conducted by phone between March 15 and April 24, 2011, 25% of American college graduates said that their student loans make it harder for them to buy a home (Time, May 30, 2011). Suppose that this result is true for
Let µ be the mean annual salary of Major League Baseball players for 2012. Assume that the standard deviation of the salaries of these players is $2,845,000. What is the probability that the 2012 mean salary of a random sample of 32 baseball players was within $500,000 of the population mean, µ?
The test scores for 300 students were entered into a computer, analyzed, and stored in a file. Unfortunately, someone accidentally erased a major portion of this file from the computer. The only information that is available is that 30% of the scores were below 65 and 15% of the scores were above
A chemist has a 10-gallon sample of river water taken just downstream from the outflow of a chemical plant. He is concerned about the concentration, c (in parts per million), of a certain toxic substance in the water. He wants to take several measurements, find the mean concentration of the toxic

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