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mathematics
statistics

Questions and Answers of Statistics

Assume that the chest measurements in Exercise 6.90 are normally distributed with a mean of µ = 39.83 and standard deviation of σ = 2.05.a. What proportion of the observations would lie between
In Exercise 1.67, Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape. Suppose we assume that the temperatures of healthy humans is approximately
A Snapshot in USA Today indicates that 51% of Americans say the average person is not very considerate of others when talking on a cellphone.11 Suppose that 100 Americans are randomly selected. Find
Philatelists (stamp collectors) often buy stamps at or near retail prices, but, when they sell, the price is considerably lower. For example, depending on the mix of a collection, condition, demand,
The scores on a national achievement test were approximately normally distributed, with a mean of 540 and a standard deviation of 110. a. If you achieved a score of 680, how far, in standard
Although faculty salaries at colleges and universities in the United States continue to rise, they do not always keep pace with the cost of living and with salaries in the private sector. In 2010,
Briggs and King developed the technique of nuclear transplantation, in which the nucleus of a cell from one of the later stages of the development of an embryo is transplanted into a zygote (a
Very often, at the end of an exam that seemed particularly difficult, students will ask the professor, "Are you going to curve the grades?" Unfortunately, "curving the grades" doesn't necessarily
A population consists of N = 500 experimental units. Use a random number table to select a random sample of n = 20 experimental units. What is the probability that each experimental unit is selected
Does the race of an interviewer matter? This question was investigated by Chris Gilberg and colleagues and reported in an issue of Chance magazine. The interviewer asked, "Do you feel that
The American Journal of Human Biology reported on a study of a dietary assessment tool for use in the population of urban Native American youth. The subjects were Native American youth attending an
A small new study shows that tai chi, an ancient Chinese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The study assigned 66 fibromyalgia patients to take
Two different Gallup Polls were conducted for CNN/USA Today, both of which involved people's feelings about the U.S. space program. Here is a question from each poll, along with the responses of the
Random samples of size n were selected from populations with the means and variances given here. Find the mean and standard deviation of the sampling distribution of the sample mean in each case: a.
Refer to Exercise 7.15. a. If the sampled populations are normal, what is the sampling distribution of for parts a, b, and c? b. According to the Central Limit Theorem, if the sampled populations
A population consists of N = 5 numbers: 1, 3, 5, 6, and 7. It can be shown that the mean and standard deviation for this population are µ = 4.4 and Ïƒ = 2.15, respectively.a.
Refer to Exercise 7.17. a. Use the data entry method in your calculator to find the mean and standard deviation of the 50 values of given in Exercise 7.17, part c. b. Compare the values calculated
A random sample of n observations is selected from a population with standard deviation σ = 1. Calculate the standard error of the mean (SE) for these values of n: a. n = 1 b. n = 2 c. n = 4 d. n =
A random sample of size n = 49 is selected from a population with mean µ = 53 and standard deviation σ = 21. a. What will be the approximate shape of the sampling distribution of ? b. What will
Refer to Exercise 7.21. Find the probability that the sample mean is greater than 55.Exercise 7.21A random sample of size n = 49 is selected from a population with mean µ = 53 and standard deviation
A random sample of size n = 40 is selected from a population with mean µ = 100 and standard deviation σ = 20. a. What will be the approximate shape of the sampling distribution of ? b. What will
Refer to Exercise 7.23. Find the probability that the sample mean is between 105 and 110.Exercise 7.23A random sample of size n = 40 is selected from a population with mean µ = 100 and standard
Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 106 and standard deviation equal to 12.a. Give the mean and the standard
Suppose that college faculty with the rank of professor at public 2-year institutions earn an average of $71,802 per year with a standard deviation of $4000. In an attempt to verify this salary
When research chemists perform experiments, they may obtain slightly different results on different replications, even when the experiment is performed identically each time. These differences are
Explain why the weight of a package of one dozen tomatoes should be approximately normally distributed if the dozen tomatoes represent a random sample.
Use the Central Limit Theorem to explain why a Poisson random variable-say, the number of a particular type of bacteria in a cubic foot of water-has a distribution that can be approximated by a
A paper manufacturer requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous
The normal daily human potassium requirement is in the range of 2000 to 6000 milligrams (mg), with larger amounts required during hot summer weather. The amount of potassium in food varies, but
The total daily sales, x, in the deli section of a local market is the sum of the sales generated by a fixed number of customers who make purchases on a given day. a. What kind of probability
In Exercise 1.67, Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape. Suppose we assume that the temperatures of healthy humans are approximately normal
Sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in The
Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample
Is it appropriate to use the normal distribution to approximate the sampling distribution of in the following circumstances? a. n = 50, p = .05 b. n = 75, p = .1 c. n = 250, p = .99
Random samples of size n = 75 were selected from a binomial population with p = .4. Use the normal distribution to approximate the following probabilities:a. P( ≤ .43)b. P(.35 ≤ ≤ .43)
Random samples of size n = 500 were selected from a binomial population with p = .1.a. Is it appropriate to use the normal distribution to approximate the sampling distribution of ? Check to make
Calculate SE() for n = 100 and these values of p: a. p = .01 b. p = .10 c. p = .30 d. p = .50 e. p = .70 f. p = .90 g. p = .99 h. Plot SE() versus p on graph paper and sketch a smooth curve through
A random sample of size n = 50 is selected from a binomial distribution with population proportion p = .7.a. What will be the approximate shape of the sampling distribution of ?b. What will be the
A random sample of size n = 80 is selected from a binomial distribution with population proportion p = .25.a. What will be the approximate shape of the sampling distribution of ?b. What will be the
a. Is the normal approximation to the sampling distribution of appropriate when n = 400 and p = .8?b. Use the results of part a to find the probability that is greater than .83.c. Use the results
Recycling trash, reducing waste, and reusing materials are eco-actions that will help the environment. According to a USA Today snapshot (Exercise 6.45), 78% of respondents list recycling as the
Parents with children list a GPS system (28%) and a DVD player (28%) as "must have" accessories for a road trip. Suppose a sample of n = 1000 parents are randomly selected and asked what devices they
An advertiser claims that the average percentage of brown M&M'S candies in a package of milk chocolate M&M'S is 13%. Suppose you randomly select a package of milk chocolate M&M'S that
It seems that driving with a pet in the car is the third worst driving distraction, behind talking on the phone and texting.According to an American Automobile Association study, 80% of drivers admit
Are you a chocolate "purist," or do you like other ingredients in your chocolate? American Demographics reports that almost 75% of consumers like traditional ingredients such as nuts or caramel in
a. Use the data to determine the upper and lower control limits for an chart.b. What is the purpose of an chart?c. Construct an chart for the process and explain how it can be used.
a. Use the data to determine the upper and lower control limits for an chart.b. Construct an chart for the process and explain how it can be used.
Explain the difference between an chart and a p chart.
Samples of n = 100 items were selected hourly over a 100-hour period, and the sample proportion of defectives was calculated each hour. The mean of the 100 sample proportions was .035. a. Use the
Samples of n = 200 items were selected hourly over a 100-hour period, and the sample proportion of defectives was calculated each hour. The mean of the 100 sample proportions was .041. a. Use the
A producer of brass rivets randomly samples 400 rivets each hour and calculates the proportion of defectives in the sample. The mean sample proportion calculated from 200 samples was equal to .021.
The manager of a building-supplies company randomly samples incoming lumber to see whether it meets quality specifications. From each shipment, 100 pieces of 2 Ã— 4 lumber are inspected
A coal-burning power plant tests and measures three specimens of coal each day to monitor the percentage of ash in the coal. The overall mean of 30 daily sample means and the combined standard
The data in the table are measures of the radiation in air particulates at a nuclear power plant. Four measurements were recorded at weekly intervals over a 26-week period. Use the data to construct
A hardwoods manufacturing plant has a production line designed to produce baseball bats weighing 32 ounces. During a period of time when the production process was known to be in statistical control,
A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 500 questionnaires were returned, and of the 500 returned, 360 respondents were strongly opposed to a surcharge
A finite population consists of four elements: 6, 1, 3, 2.a. How many different samples of size n = 2 can be selected from this population if you sample without replacement? (Sampling is said to be
Refer to Exercise 7.60. Find the sampling distribution for if random samples of size n = 3 are selected without replacement. Graph the sampling distribution of . Exercise 7.60 A finite population
Suppose a random sample of n = 5 observations is selected from a population that is normally distributed, with mean equal to 1 and standard deviation equal to .36.a. Give the mean and standard
A certain type of automobile battery is known to last an average of 1110 days with a standard deviation of 80 days. If 400 of these batteries are selected, find the following probabilities for the
Studies indicate that drinking water supplied by some old lead-lined city piping systems may contain harmful levels of lead. An important study of the Boston water supply system showed that the
Studies indicate that the earth's vegetative mass, or biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m2), may in fact be too high and that tropical biomass
The safety requirements for hard hats worn by construction workers and others, established by the American National Standards Institute (ANSI), specify that each of three hats pass the following
A research psychologist is planning an experiment to determine whether the use of imagery-picturing a word in your mind-affects people's ability to memorize. He wants to use two groups of subjects: a
The results of a CBS News Poll concerning views on same-sex marriage and gay rights given in the table that follows show that there is no consensus on this issue among Americans.a. Is this an
A biology experiment was designed to determine whether sprouting radish seeds inhibit the germination of lettuce seeds. Three 10-centimeter Petri dishes were used. The first contained 26 lettuce
A study of about n = 1000 individuals in the United States during September 21-22, 2001, revealed that 43% of the respondents indicated that they were less willing to fly following the events of
Suppose a telephone company executive wishes to select a random sample of n = 20 out of 7000 customers for a survey of customer attitudes concerning service. If the customers are numbered for
The proportion of individuals with an Rh-positive blood type is 85%. You have a random sample of n = 500 individuals. a. What are the mean and standard deviation of , the sample proportion with
What survey design is used in each of these situations? a. A random sample of n = 50 city blocks is selected, and a census is done for each single-family dwelling on each block. b. The highway patrol
The maximum load (with a generous safety factor) for the elevator in an office building is 2000 pounds. The relative frequency distribution of the weights of all men and women using the elevator is
The number of wiring packages that can be assembled by a company's employees has a normal distribution, with a mean equal to 16.4 per hour and a standard deviation of 1.3 per hour. a. What are the
Refer to Exercise 7.75. Suppose the company employs 10 assemblers of wiring packages. a. Find the mean and standard deviation of the company's daily (8-hour day) production of wiring packages. b.
The table lists the number of defective 60-watt light-bulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during this time the manufacturing process
A hardware store chain purchases large shipments of light-bulbs from the manufacturer described in Exercise 7.77 and specifies that each shipment must contain no more than 4% defectives. When the
One question on a survey questionnaire is phrased as follows: "Don't you agree that there is too much sex and violence during prime TV viewing hours?" Comment on possible problems with the responses
During long production runs of canned tomatoes, the average weights (in ounces) of samples of five cans of standard- grade tomatoes in pureed form were taken at 30 control points during an 11-day
An experimenter wants to find an appropriate temperature at which to store fresh strawberries to minimize the loss of ascorbic acid. There are 20 storage containers, each with controllable
A bottler of soft drinks packages cans in six-packs. Suppose that the fill per can has an approximate normal distribution with a mean of 12 fluid ounces and a standard deviation of 0.2 fluid
Packages of food whose average weight is 16 ounces with a standard deviation of 0.6 ounces are shipped in boxes of 24 packages. If the package weights are approximately normally distributed, what is
A manufacturing process is designed to produce an electronic component for use in small portable television sets. The components are all of standard size and need not conform to any measurable
Contrary to current thought about omega-3 fatty acids, new research shows that the beneficial fats may not help reduce second heart attacks in heart attack survivors. The study included 4837 men and
The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is widely used in business and
Explain what is meant by "margin of error" in point estimation.
Suppose you are writing a questionnaire for a sample survey involving n = 100 individuals. The questionnaire will generate estimates for several different binomial proportions. If you want to report
Partly because of our addiction to fast food, the average American consumes 32.7 pounds of cheese, 14.0 pounds of ice cream, and drinks 48.8 gallons of soda each year, according to the 2010
Even though we know it may not be good for us, many Americans really enjoy their fast food! A survey conducted by Pew Research Center graphically illustrated our penchant for eating out, and in
In an article in the Annals of Botany, a researcher reported the basal stem diameters of two groups of dicot sunflowers: those that were left to sway freely in the wind and those that were
In a regular NBA season, each team plays 82 games, some at home and some on the road. Can you afford the price of a ticket? The Web site wiki.answers.com indicates that the low prices are around $10
A dean of men wishes to estimate the average cost of the freshman year at a particular college correct to within $500, with a probability of .95. If a random sample of freshmen is to be selected and
A quality-control engineer wants to estimate the fraction of defectives in a large lot of printer ink cartridges. From previous experience, he feels that the actual fraction of defectives should be
Samples of 400 printed circuit boards were selected from each of two production lines A and B. Line A produced 40 defectives, and line B produced 80 defectives. Estimate the difference in the actual
Refer to Exercise 8.106. Suppose 10 samples of n = 400 printed circuit boards were tested and a confidence interval was constructed for p for each of the 10 samples. What is the probability that
G. Wayne Marino investigated some of the variables related to "fast starts," the acceleration and speed of a hockey player from a stopped position. Sixty-nine hockey players, varsity and intramural,
Exercise 8.108 presented statistics from a study of fast starts by ice hockey skaters. The mean and standard deviation of the 69 individual average acceleration measurements over the 6-meter distance
A random sample of n = 900 observations from a binomial population produced x = 655 successes. Estimate the binomial proportion p and calculate the margin of error.
The mean and standard deviation of the speeds of the sample of 69 skaters at the end of the 6-meter distance in Exercise 8.108 were 5.753 and .892 meters per second, respectively. a. Find a 95%
In addition to teachers and administrative staff, schools also have many other employees, including bus drivers, custodians, and cafeteria workers. In Auburn, WA, the average hourly wage is $16.92
An experimental rehabilitation technique was used on released convicts. It was shown that 79 of 121 men subjected to the technique pursued useful and crime-free lives for a 3-year period following
If 36 measurements of the specific gravity of aluminum had a mean of 2.705 and a standard deviation of .028, construct a 98% confidence interval for the actual specific gravity of aluminum.

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