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mathematics
statistics

Questions and Answers of Statistics

Let x be a binomial random variable with n = 10 and p = .4. Find these values:a. P(x = 4)b. P(x ≥ 4)c. P(x > 4)d. P(x ≤ 4)e. µ = npf. σ = √npq
A West Coast university has found that about 90% of its accepted applicants for enrollment in the freshman class will actually enroll. In 2012, 1360 applicants were accepted to the university. Within
Suppose that one out of every 10 homeowners in the state of California has invested in earthquake insurance. If 15 homeowners are randomly chosen to be interviewed, a. What is the probability that at
Improperly wired control panels were mistakenly installed on two of eight large automated machine tools. It is uncertain which of the machine tools have the defective panels, and a sample of four
How do you survive when there's no time to eat-fast food, no food, a protein bar, candy? A Snapshot in USA Today indicates that 36% of women aged 25-55 say that, when they are too busy to eat, they
According to a USA Today Snapshot, drivers say fixing or repaving streets is the best way to make their communities drivable-better than building new roads or adding lanes. Suppose that n = 15
The recession has caused many people to use their credit cards far less. In fact, in the United States, 60% of consumers say they are committed to living with fewer credit cards. A sample of n = 400
A new surgical procedure is said to be successful 80% of the time. Suppose the operation is performed five times and the results are assumed to be independent of one another. What are the
Refer to Exercise 5.96. If less than two operations were successful, how would you feel about the performance of the surgical team? Exercise 5.96 A new surgical procedure is said to be successful 80%
Suppose the four engines of a commercial aircraft are arranged to operate independently and that the probability of in-flight failure of a single engine is .01. What is the probability of the
Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 10 young adults were randomly selected and their preferences recorded. a. What is
How safe is it to live near a nuclear reactor? Men who lived in a coastal strip that extends 20 miles north from a nuclear reactor in Plymouth, Massachusetts, developed some forms of cancer at a rate
Consider a standard normal random variable with µ = 0 and standard deviation σ = 1. Use Table 3 to find the following probabilities: a. P(z < 2) b. P(z > 1.16) c. P(- 2.33 < z < 2.33) d. P(z < 1.88)
a. Find a z0 such that P(- z0 < z < z0) = .90. b. Find a z0 such that P(- z0 < z < z0) = .99.
Find the following percentiles for the standard normal random variable z: a. 90th percentile b. 95th percentile c. 98th percentile d. 99th percentile
A normal random variable x has mean µ = 10 and standard deviation σ = 2. Find the probability associated with each of the following intervals. a. x > 13.5 b. x = 8.2 c. 9.4 < x < 10.6
A normal random variable x has mean µ = 1.2 and standard deviation σ = .15. Find the probability associated with each of the following intervals. a. 1.00 < x < 1.10 b. x > 1.38 c. 1.35 < x < 1.50
A normal random variable x has an unknown mean m and standard deviation σ = 2. If the probability that x exceeds 7.5 is .8023, find µ.
A normal random variable x has mean 35 and standard deviation 10. Find a value of x that has area .01 to its right. This is the 99th percentile of this normal distribution.
A normal random variable x has mean 50 and standard deviation 15. Would it be unusual to observe the value x = 0? Explain your answer.
A normal random variable x has an unknown mean and standard deviation. The probability that x exceeds 4 is .9772, and the probability that x exceeds 5 is .9332. Find µ and σ.
The meat department at a local supermarket specifically prepares its "1-pound" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1
Human heights are one of many biological random variables that can be modeled by the normal distribution. Assume that the heights of American men have a mean of 69.5 inches and a standard deviation
Find these probabilities associated with the standard normal random variable z: a. P(z > 5) b. P(- 3 < z < 3) c. P(z < 2.81) d. P(z > 2.81)
The diameters of Douglas firs grown at a Christmas tree farm are normally distributed with a mean of 4 inches and a standard deviation of 1.5 inches. a. What proportion of the trees will have
Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16. a. What proportion of healthy people will have CBF readings between
For a car traveling 30 miles per hour (mph), the distance required to brake to a stop is normally distributed with a mean of 50 feet and a standard deviation of 8 feet. Suppose you are traveling 30
Suppose that you must establish regulations concerning the maximum number of people who can occupy an elevator. A study indicates that if eight people occupy the elevator, the probability
The discharge of suspended solids from a phosphate mine is normally distributed, with a mean daily discharge of 27 milligrams per liter (mg/l) and a standard deviation of 14 mg/l. On what proportion
An experimenter publishing in the Annals of Botany investigated whether the stem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or
The number of times x an adult human breathes per minute when at rest has a probability distribution that is approximately normal, with the mean equal to 16 and the standard deviation equal to 4. If
One method of arriving at economic forecasts is to use a consensus approach. A forecast is obtained from each of a large number of analysts, and the average of these individual forecasts is the
How does the IRS decide on the percentage of income tax returns to audit for each state? Suppose they do it by randomly selecting 50 values from a normal distribution with a mean equal to 1.55% and a
Suppose the numbers of a particular type of bacteria in samples of 1 milliliter (ml) of drinking water tend to be approximately normally distributed, with a mean of 85 and a standard deviation of 9.
Calculate the area under the standard normal curve to the left of these values: a. z = 1.6 b. z = 1.83 c. z = .90 d. z = 4.18
A grain loader can be set to discharge grain in amounts that are normally distributed, with mean m bushels and standard deviation equal to 25.7 bushels. If a company wishes to use the loader to fill
A publisher has discovered that the number of words contained in new manuscripts is normally distributed, with a mean equal to 20,000 words in excess of that specified in the author's contract and a
A stringer of tennis rackets has found that the actual string tension achieved for any individual racket will vary as much as 6 pounds per square inch from the desired tension set on the stringing
An article in American Demographics claims that more than twice as many shoppers are out shopping on the weekends than during the week. Not only that, such shoppers also spend more money on their
What's a normal pulse rate? That depends on a variety of factors. Pulse rates between 60 and 100 beats per minute are considered normal for children over 10 and adults. Suppose that these pulse rates
Consider a binomial random variable x with n = 25 and p = .6. a. Can the normal approximation be used to approximate probabilities in this case? Why or why not? b. What are the mean and standard
Consider a binomial random variable x with n = 45 and p = .05. a. Are np and nq both larger than 5? b. Based on your answer to part a, can we use the normal approximation to approximate the binomial
Let x be a binomial random variable with n = 25 and p = .3. a. Is the normal approximation appropriate for this binomial random variable? b. Find the mean and standard deviation for x. c. Use the
Let x be a binomial random variable with n = 15 and p = .5.a. Is the normal approximation appropriate?b. Find P(x ≥ 6) using the normal approximation.c. Find P(x > 6) using the normal
Let x be a binomial random variable with n = 100 and p = .2. Find approximations to these probabilities: a. P(x > 22) b. P(x ≥ 22) c. P(20 < x < 25) d. P(x ≤ 25)
Calculate the area under the standard normal curve between these values: a. z = - 1.4 and z = 1.4 b. z = - 3.0 and z = 3.0
Let x be a binomial random variable with n = 25, p = .2. a. Use Table 1 in Appendix I to calculate P(4 ≤ x ≤ 6). b. Find µ and σ for the binomial probability distribution, and use the normal
Suppose the random variable x has a binomial distribution corresponding to n = 20 and p = .30. Use Table 1 of Appendix I to calculate these probabilities: a. P(x = 5) b. P(x ≥ 7)
Refer to Exercise 6.41. Use the normal approximation to calculate P(x = 5) and P(x ≥ 7). Compare with the exact values obtained from Table 1 in Appendix I.
Consider a binomial experiment with n = 20 and p = .4. Calculate P(x ≥ 10) using each of these methods: a. Table 1 in Appendix I b. The normal approximation to the binomial probability distribution
Find the normal approximation to P(355 ≤ x ≤ 360) for a binomial probability distribution with n = 400 and p = .9.
Are you helping to save the environment? A USA Today Snapshot found that about 78% of Americans believe that recycling trash makes the biggest difference in protecting the environment.Suppose a
Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x = 60 children with the defect in a total of
Airlines and hotels often grant reservations in excess of capacity to minimize losses due to no-shows. Suppose the records of a hotel show that, on the average, 10% of their prospective guests will
Compilation of large masses of data on lung cancer shows that approximately 1 of every 40 adults acquires the disease. Workers in a certain occupation are known to work in an air-polluted environment
Do Americans tend to vote for the taller of the two major candidates in a presidential election? In 49 of our presidential elections for which the heights of all the major-party candidates are known,
Find the following probabilities for the standard normal random variable z: a. P(- 1.43 < z < .68) b. P(.58 < z < 1.74) c. P(- 1.55 < z < - .44) d. P(z > 1.34) e. P(z < - 4.32)
In a certain population, 15% of the people have Rh-negative blood. A blood bank serving this population receives 92 blood donors on a particular day. a. What is the probability that 10 or fewer are
Two of the biggest soft drink rivals, Pepsi and Coke, are very concerned about their market shares. The pie chart that follows claims that PepsiCo's share of the beverage market is 25%.6 Assume that
In a study conducted for the Center for a New American Dream, Time magazine reports that 60% of Americans felt pressure to work too much, and 80% wished for more family time.7 Assume that these
The article in Time magazine7 (Exercise 6.52) also reported that 80% of men and 62% of women put in more than 40 hours a week on the job. Assume that these percentages are correct for all Americans,
Calculate the area under the standard normal curve to the left of these values: a. z = - .90 b. z = 2.34 c. z = 5.4
Calculate the area under the standard normal curve between these values: a. z = - 2.0 and z = 2.0 b. z = - 2.3 and z = - 1.5
Find the following probabilities for the standard normal random variable z: a. P(- 1.96 ≤ z ≤ 1.96) b. P(z >1.96) c. P(z < - 1.96)
a. Find a z0 such that P(z > z0) = .9750. b. Find a z0 such that P(z > z0) = .3594.
a. Find a z0 such that P(- z0 ≤ z ≤ z0) = .95. b. Find a z0 such that P(- z0 ≤ z ≤ z0) = .98. c. Find a z0 such that P(- z0 ≤ z ≤ z0) = .90. d. Find a z0 such that P(- z0 ≤ z ≤ z0) =
A normal random variable x has mean µ = 5 and standard deviation σ = 2. Find the probabilities associated with the following intervals: a. 1.2 < x < 10 b. x > 7.5 c. x ≤ 0
Find these probabilities for the standard normal random variable z:a. P(z < 2.33)b. P(z < 1.645)c. P(z > 1.96)d. P(- 2.58 < z < 2.58)
Let x be a binomial random variable with n = 36 and p = .54. Use the normal approximation to find: a. P(x ≤ 25) b. P(15 ≤ x ≤ 20) c. P(x > 30)
Using Table 3 in Appendix I, calculate the area under the standard normal curve to the left of the following: a. z = 1.2 b. z = - .9 c. z = 1.46 d. z = - .42
Find the following probabilities for the standard normal random variable: a. P(.3 < z < 1.56) b. P(- .2 < z < .2)
Find z0 such that P(z > z0) = .5.
Find z0 such that P(- z0 < z < z0) = .5. What percentiles do - z0 and z0 represent?
It is estimated that the mean life span of oil-drilling bits is 75 hours. Suppose an oil exploration company purchases drill bits that have a life span that is approximately normally distributed with
The influx of new ideas into a college or university, introduced primarily by new young faculty, is becoming a matter of concern because of the increasing ages of faculty members. That is, the
A machine operation produces bearings whose diameters are normally distributed, with mean and standard deviation equal to .498 and .002, respectively. If specifications require that the bearing
a. Find a z0 such that P(z > z0) = .025. b. Find a z0 such that P(z < z0) = .9251.
A used-car dealership has found that the length of time before a major repair is required on the cars it sells is normally distributed with a mean equal to 10 months and a standard deviation of 3
The daily sales total (excepting Saturday) at a small restaurant has a probability distribution that is approximately normal, with a mean µ equal to $1230 per day and a standard deviation σ equal
The life span of a type of automatic washer is approximately normally distributed with mean and standard deviation equal to 10.5 and 3.0 years, respectively. If this type of washer is guaranteed for
Most users of automatic garage door openers activate their openers at distances that are normally distributed with a mean of 30 feet and a standard deviation of 11 feet. To minimize interference with
The average length of time required to complete a college achievement test was found to equal 70 minutes with a standard deviation of 12 minutes. When should the test be terminated if you wish to
The length of time required to run a 5000-mile check and to service an automobile has a mean equal to 1.4 hours and a standard deviation of .7 hour. Suppose that the service department plans to
An advertising agency has stated that 20% of all television viewers watch a given program. In a random sample of 1000 viewers, x = 184 viewers were watching the program. Do these data present
A researcher notes that senior corporation executives are not very accurate forecasters of their own annual earnings. He states that his studies of a large number of company executive forecasts
A soft drink machine can be regulated to discharge an average of µ ounces per cup. If the ounces of fill are normally distributed, with standard deviation equal to .3 ounce, give the setting for µ
A manufacturing plant uses light bulbs whose life spans are normally distributed, with mean and standard deviation equal to 500 and 50 hours, respectively. In order to minimize the number of bulbs
Find a z0 such that P(- z0 < z < z0) = .8262.
The admissions office of a small college is asked to accept deposits from a number of qualified prospective freshmen so that, with probability about .95, the size of the freshman class will be less
An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline sells 160 tickets for a flight that has only 155 seats, what is the
It is known that 30% of all calls coming into a telephone exchange are long-distance calls. If 200 calls come into the exchange, what is the probability that at least 50 will be long-distance calls?
In Exercise 5.75, a cross between two peony plants-one with red petals and one with streaky petals-produced offspring plants with red petals 75% of the time. Suppose that 100 seeds from this cross
A purchaser of electric relays buys from two suppliers, A and B. Supplier A supplies two of every three relays used by the company. If 75 relays are selected at random from those in use by the
Psychologists believe that excessive eating may be associated with emotional states (being upset or bored) and environmental cues (watching television, reading, and so on). To test this theory,
The Biology Data Book reports that the gestation time for human babies averages 278 days with a standard deviation of 12 days. Suppose that these gestation times are normally distributed. a. Find the
In Exercise 6.28, we suggested that the IRS assigns auditing rates per state by randomly selecting 50 auditing percentages from a normal distribution with a mean equal to 1.55% and a standard
Among the 10 most popular sports, men include competition-type sports-pool and billiards, basketball, and softball-whereas women include aerobics, running, hiking, and calisthenics. However, the top
A psychological introvert-extrovert test produced scores that had a normal distribution with a mean and standard deviation of 75 and 12, respectively. If we wish to designate the highest 15% as
a. Find a z0 that has area .9505 to its left. b. Find a z0 that has area .05 to its left.
The chest measurements for 5738 Scottish militiamen in the early 19th century are given below. Chest sizes are measured in inches, and each observation reports the number of soldiers with that chest

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