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elementary statistics

Elementary Statistics Using Excel Pearson New 5th Edition Mario F Triola - Solutions

Sampling Distribution Data Set 20 in the Appendix: Data Sets includes a sample of weights of 100 M&M candies. If we explore this sample of 100 weights by constructing a histogram and finding the mean and standard deviation, do those results describe the sampling distribution of the mean? Why or why
Unbiased Estimators Data Set 1 in the Appendix: Data Sets includes a sample of 40 pulse rates of women. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median;
Sampling with Replacement In a recent year, the U.S. Mint in Denver manufactured 270 million quarters. As part of the mint’s quality control program, samples of quarters are randomly selected each day for detailed inspection to confirm that they meet all required specifications.a. Do you think
Minting Quarters In a recent year, the U.S. Mint in Denver manufactured 270 million quarters. Assume that on each day of production, a sample of 50 quarters is randomly selected, and the mean weight is obtained.a. Given that the population of quarters has a mean weight of 5.67 g, what do you know
SAT and ACT Tests Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312.Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to
Outliers For the purposes of constructing modified boxplots, outliers are defined as data values that are above Q3 by an amount greater than 1.5 * IQR or below Q1 by an amount greater than 1.5 * IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that
Using Continuity Correction There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values.In such cases, we can use this continuity correction: Represent each whole number by the interval extending from 0.5 below the
Curving Test Scores A statistics professor gives a test and finds that the scores are normally distributed with a mean of 40 and a standard deviation of 10.She plans to curve the scores.a. If she curves by adding 35 to each grade, what is the new mean? What is the new standard deviation?b. Is it
Appendix: Data Sets: Weights of Diet Pepsi Refer to Data Set 19 in the Appendix:Data Sets and use the weights (pounds) of diet Pepsi.a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal.b. Treating the unrounded values of the mean and standard
Appendix: Data Sets: Pulse Rates of Males Refer to Data Set 1 in the Appendix:Data Sets and use the pulse rates of males.a. Find the mean and standard deviation, and verify that the pulse rates have a distribution that is roughly normal.b. Treating the unrounded values of the mean and standard
Quarters After 1964, quarters were manufactured so that the weights had a mean of 5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If many counterfeit coins are found, you can narrow the range of
Chocolate Chip Cookies The numbers of chocolate chips in Chips Ahoy regular cookies have a distribution that is approximately normal with a mean of 24.0 chocolate chips and a standard deviation of 2.6 chocolate chips. Find P1 and P99. How might those values be helpful to the producer of Chips Ahoy
Aircraft Seat Width Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in.
Earthquakes Based on Data Set 16 in the Appendix: Data Sets, assume that Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.184 and a standard deviation of 0.587.a. Earthquakes with magnitudes less than 2.000 are considered “microearthquakes” that are not felt.
Body Temperatures Based on the sample results in Data Set 3 in the Appendix: Data Sets, assume that human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F.a. Bellevue Hospital in New York City uses 100.6°F as the lowest temperature considered
Lengths of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.a. One classical use of the normal distribution is inspired by a letter to “Dear Abby” in which a wife claimed to have given birth 308 days after a brief visit
Designing a Work Station A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work table, we must consider sitting knee height, which is the distance from the bottom of
Water Taxi Safety When a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst-case” scenario in which all of the
Executive Jet Doorway The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 in.a. What percentage of adult men can fit through the door without bending?b. What percentage of adult women can fit through the door without bending?c. Does the door design with a
Disney Characters Most of the live characters at Disney World have height requirements with a minimum of 4 ft 8 in. and a maximum of 6 ft 3 in.a. Find the percentage of women meeting the height requirement.b. Find the percentage of men meeting the height requirement.c. If the height requirements
Air Force Pilots The U.S. Air Force requires that pilots have heights between 64 in. and 77 in.a. Find the percentage of women meeting the height requirement.b. Find the percentage of men meeting the height requirement.c. If the Air Force height requirements are changed to exclude only the tallest
Navy Pilots The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in.a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall?b. Find the percentage of men meeting the height requirement. Are many men
Mensa Mensa International calls itself “the international high IQ society,” and it has more than 100,000 members. Mensa states that “candidates for membership of Mensa must achieve a score at or above the 98th percentile on a standard test of intelligence (a score that is greater than that
Find the third quartile Q3, which is the IQ score separating the top 25% from the others.IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a randomly selected adult, find
Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%.IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a randomly selected adult,
Find P90, which is the IQ score separating the bottom 90% from the top 10%.IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a randomly selected adult, find the indicated
Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal ).IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a
Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range).IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a
Find the probability of an IQ greater than 70 (the requirement for being a statistics textbook author).IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a randomly selected
Find the probability of an IQ less than 85.IQ Scores. In Exercises 13–20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).For a randomly selected adult, find the indicated probability or IQ score. Round IQ
IQ Scores. In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Normal Distributions What is the difference between a standard normal distribution and a nonstandard normal distribution?
IQ Scores The Wechsler Adult Intelligence Scale is an IQ score obtained through a test, and the scores are normally distributed with a mean of 100 and a standard deviation of 15.A bell-shaped graph is drawn to represent this distribution.a. For the bell-shaped graph, what is the area under the
Pulse Rates Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute (based on Data Set 1 in the Appendix: Data Sets).a. What are the values of the mean and standard deviation after converting all pulse rates of women to z
For this continuous uniform distribution, find the probability of randomly selecting a value between -1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution. Does the distribution affect the results very much?
For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that area. within 1 standard deviation of the mean.b. more than 2 standard deviations away from the mean.c. within 1.96 standard deviations of the mean.d. between m -
About % of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard deviations of the mean).Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill
About % of the area is between z = -3 and z = 3 (or within 3 standard deviations of the mean).Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the
About % of the area is between z = -2 and z = 2 (or within 2 standard deviations of the mean).Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the
About % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).
z0.03 Finding Critical Values. In Exercises 41–44, find the indicated critical value.
z0.05 Finding Critical Values. In Exercises 41–44, find the indicated critical value.
z0.01 Finding Critical Values. In Exercises 41–44, find the indicated critical value.
z0.025 Finding Critical Values. In Exercises 41–44, find the indicated critical value.
Find the bone density scores that can be used as cutoff values separating the most extreme 1%of all scores. Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and
If bone density scores in the bottom 2.5% and the top 2.5% are used as cutoff points for levels that are too low or too high, find the two readings that are cutoff values. Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone
Find P5, the 5th percentile. This is the bone density score separating the bottom 5% from the top 95%. Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a
Find P90, the 90th percentile. This is the bone density score separating the bottom 90% from the top 10%. Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a
Less than 0 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given scores. If
Greater than 0 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given scores.
Greater than -3.80 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Less than 3.65 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given scores.
Between -3.90 and 2.00 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between -2.11 and 4.00 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between -0.62 and 1.78 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between -2.20 and 2.50 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between -1.93 and -0.45 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the
Between and -2.75 and -2.00 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the
Between 1.23 and 2.37 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between 0.25 and 1.25 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Greater than -0.84 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Greater than -1.50 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Greater than 1.82 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Greater than 0.82 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Less than 1.96 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given scores.
Less than 2.33 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given scores.
Less than -0.19 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Less than -2.04 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1.In each case, draw a graph and find the probability of the given
Between 1.5 minutes and 4.5 minutes Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 2 and described in Example 1.Assume that a subway passenger is randomly selected, and find the probability that the waiting time is within the
Between 1 minute and 3 minutes Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 2 and described in Example 1.Assume that a subway passenger is randomly selected, and find the probability that the waiting time is within the given
Less than 0.75 minutes Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 2 and described in Example 1.Assume that a subway passenger is randomly selected, and find the probability that the waiting time is within the given range.
Greater than 1.25 minutes Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 2 and described in Example 1.Assume that a subway passenger is randomly selected, and find the probability that the waiting time is within the given range.
Notation What does the notation za indicate?
Standard Normal Distribution Identify the requirements necessary for a normal distribution to be a standard normal distribution.
Normal Distribution A normal distribution is informally described as a probability distribution that is “bell-shaped” when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Normal Distribution When we refer to a “normal” distribution, does the word normal have the same meaning as in ordinary language, or does it have a special meaning in statistics?What exactly is a normal distribution?
Phone Calls In the month preceding the creation of this exercise, the author made 18 phone calls in 30 days. No calls were made on 17 days, 1 call was made on 8 days, and 2 calls were made on 5 days.a. Find the mean number of calls per day.b. Use the Poisson distribution to find the probability of
Expected Value for a Magazine Sweepstakes Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000),$5,000 (1 chance in 36,667,000), and $2,500 (1
Expected Value for Deal or No Deal In the television game show Deal or No Deal, contestant Elna Hindler had to choose between acceptance of an offer of $193,000 or continuing the game. If she continued to refuse all further offers, she would have won one of these five equally likely prizes: $75,
If the corresponding probabilities are 0.026, 0.154, 0.346, 0.246, and 0.130, does the given information describe a probability distribution? Why or why not?
Brand Recognition In a study of brand recognition of the Kindle eReader, four consumers are interviewed. If x is the number of consumers in the group who recognize the Kindle brand name, then x can be 0, 1, 2, 3, or
Tinnitus Find the mean and standard deviation for the random variable x. Use the range rule of thumb to identify the range of usual values for the number of males with tinnitus among four randomly selected males. Is it unusual to get three males with tinnitus among four randomly selected males?
Brown Eyes When randomly selecting 600 people, the probability of exactly 239 people with brown eyes is P(239) = 0.0331. Also, P(239 or fewer) = 0.484.Which of those two probabilities is relevant for determining whether 239 is an unusually low number of people with brown eyes? Is 239 an unusually
Brown Eyes Groups of 600 people are randomly selected. Find the mean and standard deviation for the numbers of people with brown eyes in such groups, then use the range rule of thumb to identify the range of usual values for those with brown eyes. For such a group of 600 randomly selected people,
Brown Eyes Find the probability that among six randomly selected people, exactly four of them have brown eyes.
Brown Eyes If six people are randomly selected, find the probability that none of them has brown eyes.
Is 5 an unusually high number of flights arriving on time?
Is 0 an unusually low number of flights arriving on time?
What is the probability that at least three of the five flights arrive on time?
What does the probability of 0+ indicate? Does it indicate that among five randomly selected flights, it is impossible that none of them arrives on time?
Does the table describe a probability distribution?
Using the same SAT questions described in Exercise 2, find the standard deviation for the numbers of correct answers for those who make random guesses for all 100 questions.
There are 100 questions from an SAT test, and they are all multiple choice with possible answers ofa, b,c, d,e. For each question, only one answer is correct. Find the mean number of correct answers for those who make random guesses for all 100 questions.
Is a probability distribution defined if the only possible values of a random variable are 0, 1, 2, 3, and P(0) = P(1) = P(2) = P(3) = 0.25?
Poisson Approximation to Binomial Distribution An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6.a. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times? Why or why not?b. If
Chocolate Chip Cookies Consider an individual chocolate chip cookie to be the specified interval unit required for a Poisson distribution, and consider the variable x to be the number of chocolate chips in a cookie. Suppose the numbers of chocolate chips in 40 different reduced fat Chips Ahoy
Chocolate Chip Cookies In the production of chocolate chip cookies, we can consider each cookie to be the specified interval unit required for a Poisson distribution, and we can consider the variable x to be the number of chocolate chips in a cookie. Suppose the numbers of chocolate chips in 34
Disease Cluster Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children.a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in
World War II Bombs In Exercise 1 we noted that in analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions.a. Find the probability that a randomly selected region had
Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After

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