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mathematics
statistics

Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions

The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probability that a randomly selected teacher earnsa. Between $35,000 and $45,000 a year 0.3031b. More than $40,000 a year 0.9131c. If you were applying
If the average price of a new one family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 80% of the market. Assume that the variable is normally distributed.
The average price of a personal computer (PC) is $949. If the computer prices are approximately normally distributed and σ = $100, what is the probability that a randomly selected PC costs more than $1200? The least expensive 10% of personal computers cost less than what amount?
To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 122.6, find the
An automobile dealer finds that the average price of a previously owned vehicle is $8256. He decides to sell cars that will appeal to the middle 60% of the market in terms of price. Find the maximum and minimum prices of the cars the dealer will sell. The standard deviation is $1150, and the
The average length of a hospital stay for all diagnoses is 4.8 days. If we assume that the lengths of hospital stays are normally distributed with a variance of 2.1, then 10% of hospital stays are longer than how many days? Thirty percent of stays are less than how many days?
Competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100.a. The top 3% of students receive $500. What is the minimum score you would need to receive this award?b. The bottom 1.5% of students must go to summer school. What is the minimum
Americans drank an average of 23.2 gallons of bottled water per capita in 2008. If the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly selected American drank more than 25 gallons of bottled water. What is the probability that the
The mean lifetime of a wristwatch is 25 months, with a standard deviation of 5 months. If the distribution is normal, for how many months should a guarantee be made if the manufacturer does not want to exchange more than 10% of the watches? Assume the variable is normally distributed.
The average daily jail population in the United States is 706,242. If the distribution is normal and the standard deviation is 52,145, find the probability that on a randomly selected day, the jail population isa. Greater than 750,000 0.2005 (TI: 0.2007)b. Between 600,000 and 700,000
To qualify for a police academy, applicants are given a test of physical fitness. The scores are normally distributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected, find the cutoff score.
In the distributions shown, state the mean and standard deviation for each. Hint: See Figures 6–5 and 6–6. Also the vertical lines are 1 standard deviation apart.a.b.c.
In a normal distribution, find σ when µ = 105 and 5.48% of the area lies to the right of 110.
In a certain normal distribution, 1.25% of the area lies to the left of 42, and 1.25% of the area lies to the right of 48. Find µand σ.
An instructor gives a 100-point examination in which the grades are normally distributed. The mean is 60 and the standard deviation is 10. If there are 5% A’s and 5% F’s, 15% B’s and 15% D’s, and 60% C’s, find the scores that divide the distribution into those categories.
The data shown represent the number of outdoor drive-in movies in the United States for a 14-year period. Check for normality.2084 1497 1014 910 899 870 837 859848
The national average SAT score (for Verbal and Math) is 1028. If we assume a normal distribution with σ = 92, what is the 90th percentile score? What is the probability that a randomly selected score exceeds 1200?
The data shown represent the cigarette tax (in cents) for 50 selected states. Check for normality.
The data shown represent the box office total revenue (in millions of dollars) for a randomly selected sample of the top-grossing films in 2009. Check for normality.
The data shown represent the number of runs made each year during Bill Mazeroski’s career. Check for normality.30 59 69 50 58 71 55 43 66 52 56 6236 13 29 17 3
The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with σ = 10 . Find the probability that a randomly selected chocolate bar will have a. Between 200 and 220 calories b. Less than 200 calories
The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment isa. More than $1000
The average salary for a Queens College full professor is $85,900. If the average salaries are normally distributed with a standard deviation of $11,000, find these probabilities. a. The professor makes more than b. The professor makes more than $75,000. Source: AAUP, Chronicle of Higher Education.
Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities.a. The student makes more than $15,000. b. The student makes between $13,000 and $14,000.
The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. What is the probability that the vehicle was driven more than 15,000 miles?
Explain why a normal distribution can be used as an approximation to a binomial distribution. What conditions must be met to use the normal distribution to approximate the binomial distribution? Why is a correction for continuity necessary?
College students often make up a substantial portion of the population of college cities and towns. State College, Pennsylvania, ranks first with 71.1% of its population made up of college students. What is the probability that in a random sample of 150 people from State College, more than 50 are
Women comprise 80.3% of all elementary school teachers. In a random sample of 300 elementary teachers, what is the probability that less than three-fourths are women?
Seventy-eight percent of U.S. homes have a telephone answering device. In a random sample of 250 homes, what is the probability that fewer than 50 do not have a telephone answering device?
The mayor of a small town estimates that 35% of the residents in the town favor the construction of a municipal parking lot. If there are 350 people at a town meeting, find the probability that at least 100 favor construction of the parking lot. Based on your answer, is it likely that 100 or more
According to the U.S. Census, 67.5% of the U.S. population was born in their state of residence. In a random sample of 200 Americans, what is the probability that fewer than 125 were born in their state of residence?
Recall that for use of a normal distribution as an approximation to the binomial distribution, the conditions np ≥ 5 and nq ≥ 5 must be met. For each given probability, compute the minimum sample size needed for use of the normal approximation.a. p = 0.1 b. p = 0.3 c. p = 0.5 d. p = 0.8 e. p =
Use the normal approximation to the binomial to find the probabilities for the specific value(s) of X.a. n = 30, p = 0.5, X = 18 b. n = 50, p = 0.8, X = 44 c. n = 100, p = 0.1, X = 12 d. n = 10, p = 0.5, X ≤ 7 e. n = 20, p = 0.7, X ≥ 12 f. n = 50, p = 0.6, X ≥ 40
Check each binomial distribution to see whether it can be approximated by a normal distribution (i.e., are ≥ 5 and ≥5?).a. n = 20, p = 0.5 b. n = 10, p = 0.6 c. n = 40, p = 0.9d. n = 50, p = 0.2 e. n = 30, p = 0.8 f. n = 20, p = 0.85
Of all 3- to 5-year-old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.
Two out of five adult smokers acquired the habit by age 14. If 400 smokers are randomly selected, find the probability that 170 or fewer acquired the habit by age 14.
A mail order company has an 8% success rate. If it mails advertisements to 600 people, find the probability of getting less than 40 sales.
A political candidate estimates that 30% of the voters in her party favor her proposed tax reform bill. If there are 400 people at a rally, find the probability that at least 100 voters will favor her tax bill. Based on your answer, is it likely that 100 or more people will favor the bill?
A political candidate estimates that 30% of the voters in her party favor her proposed tax reform bill. If there are 400 people at a rally, find the probability that at least 100 voters will favor her tax bill. Based on your answer, is it likely that 100 or more people will favor the bill?
The percentage of female Americans 25 years old and older who have completed 4 years of college or more is 26.1. In a random sample of 200 American women who are at least 25, what is the probability that at most 50 have completed 4 years of college or more?
Find the area under the standard normal distribution curve for eacha. Between z = 0 and z = 1.95 b. Between z = 0 and z = 0.37 c. Between z = 1.32 and z = 1.82d. Between z = –1.05 and z = 2.05 e. Between z = – 0.03 and z = 0.53 f. Between z = +1.10 and z = –1.80 g. To the right of z = 1.99 h.
For the first 7 months of the year, the average precipitation in Toledo, Ohio, is19.32 inches. If the average precipitation is normally distributed with a standard deviation of 2.44 inches, find these probabilities.a. A randomly selected year will have precipitation greater than 18 inches for the
Americans ate an average of 25.7 pounds of confectionary products each last year and spent an average of $61.50 per person doing so. If the standard deviation for consumption is 3.75 pounds and the standard deviation for the amount spent is $5.89, find the following:a. The probability that the
A recent study of the life span of portable compact disc players found the average to be 3.7 years with a standard deviation of 0.6 year. If a random sample of 32 people who own CD players is selected, find the probability that the mean lifetime of the sample will be less than 3.4 years. If the
Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement income. In a random sample of 120 households, what is the probability that more than 20 households but less than 35 households receive a retirement income?
The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution.
According to the government 5.3% of those employed are multiple-job holders. In a random sample of 150 people who are employed, what is the probability that fewer than 10 hold multiple jobs? What is the probability that more than 50 are not multiple-job holders?
In a large university, 30% of the incoming first-year students elect to enroll in a personal finance course offered by the university. Find the probability that of 800 randomly selected incoming first-year students, at least 260 have elected to enroll in the course.
Of the total population of the United States, 20% live in the northeast. If 200 residents of the United States are selected at random, find the probability that at least 50 live in the northeast.
Using the standard normal distribution, find each probability. (6–1)a. P (0 < z < 2.07)b. P (–1.83 < z < 0) c. P (–1.59 < z < + 2.01) d. P (1.33 < z <1.88) e. P (–2.56 < z< 0.37) f. P (z > 1.66)g. P(z < – 2.03) h. P(z > –1.19) i. P(z < 1.93) j.
The average per capita spending on health care in the United States is $5274. If the standard deviation is $600 and the distribution of health care spending is approximately normal, what is the probability that a randomly selected person spends more than $6000? Find the limits of the middle 50% of
The average salary for graduates entering the actuarial field is $40,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability thata. An individual graduate will have a salary over $45,000. b. A group of nine graduates will have a group average over
On a certain run of a commuter train, the average number of passengers is 476 and the standard deviation is 22. Assume the variable is normally distributed. If the train makes the run, find the probability that the number of passengers will bea. Between 476 and 500 passengers b. Less than 450
The average individual monthly spending in the United States for paging and messaging services is $10.15. If the standard deviation is $2.45 and the amounts are normally distributed, what is the probability that a randomly selected user of these services pays more than $15.00 per month? Between
The heights (in feet above sea level) of a random sample of the world’s active volcanoes are shown here. Check for normality.
A random sample of enrollments in Pennsylvania€™s private four-year colleges is listed here. Check for normality.
What is the difference between a point estimate and an interval estimate of a parameter? Which is better? Why?
The numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. Use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence.
In a recent study of 35 ninthgrade students, the mean number of hours per week that they played video games was 16.6. The standard deviation of the population was 2.8.a. Find the best point estimate of the mean. 16.6 hoursb. Find the 95% confidence interval of the mean of the time playing video
First-semester GPAs for a random selection of freshmen at a large university are shown. Estimate the true mean GPA of the freshman class with 99% confidence. Assume σ = 0.62.
A recent study showed that the modern working person experiences an average of 2.1 hours per day of distractions (phone calls, e-mails, impromptu visits, etc.). A random sample of 50 workers for a large corporation found that these workers were distracted an average of 1.8 hours per day and the
A sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. The population standard deviation is 2.1.a. Find the best point estimate of the mean.b. Find the 95% confidence interval of the mean number of jobs. c. Find the 99%
A survey of 35 individuals who passed the seven exams and obtained the rank of Fellow in the actuarial field finds the average salary to be $150,000. If the standard deviation for the population is $15,000, construct a 95% confidence interval for all Fellows.
A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 90% confidence. Assume σ = 31.
A study of 415 kindergarten students showed that they have seen on average 5000 hours of television. If the sample standard deviation of the population is 900, find the 95% confidence level of the mean for all students. If a parent claimed that his children watched 4000 hours, would the claim be
A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. Find the 90% confidence interval of the true mean. If a day care center were starting up and wanted to keep tuition low, what would be a
Noise levels at various area urban hospitals were measured in decibels. The mean of the noise levels in 84 corridors was 61.2 decibels, and the standard deviation of the population was 7.9. Find the 95% confidence interval of the true mean.
The growing seasons for a random sample of 35 U.S. cities were recorded, yielding a sample mean of 190.7 days and the population standard deviation of 54.2 days. Estimate the true mean population of the growing season with 95% confidence.
A random sample of shoppers at a convenience store are selected to see how much they spent on that visit. The standard deviation of the population is $6.43. How large a sample must be selected if the researcher wants to be 99% confident of finding whether the true mean differs from the sample mean
In the hospital study cited in Exercise 19, the mean noise level in the 171 ward areas was 58.0 decibels, and the population standard deviation is 4.8. Find the 90% confidence interval of the true mean.
A health care professional wishes to estimate the birth weights of infants. How large a sample must be obtained if she desires to be 90% confident that the true mean is within 2 ounces of the sample mean? Assume σ = 8 ounces.
A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.15? A previous study showed that the standard deviation of the price was $0.26.
If the variance of a national accounting examination is 900, how large a sample is needed to estimate the true mean score within 5 points with 99% confidence?
a. z a / 2 for the 99% confidence interval b. z a / 2 for the 98% confidence interval c. z a / 2 for the 95% confidence interval d. z a / 2 for the 90% confidence interval e. z a / 2 for the 94% confidence interval
A random sample of stock prices per share (in dollars) is shown. Find the 90% confidence interval for the variance and standard deviation for the prices. Assume the variable is normally distributed.
A researcher wishes to find the confidence interval of the population standard deviation for the number of homeless people in a large city. A sample of 25 months had a standard deviation of 462. Find the 95% confidence interval.
The percentage rates of home ownership for 8 randomly selected states are listed below. Estimate the population variance and standard deviation for the percentage rate of home ownership with 99% confidence.66.0 75.8 70.9 73.9 63.4
A confidence interval for a standard deviation for large samples taken from a normally distributed population can be approximated byFind the 95% confidence interval for the population standard deviation of calculator batteries. A sample of 200 calculator batteries has a standard deviation of 18
Using Table G, find the values for x2 left and x2 right.a. a = 0.05, n = 12 b. a = 0.10, n = 20 c. a = 0.05, n = 27 d. a = 0.01, n = 6 e. a = 0.10, n = 41
Find the 90% confidence interval for the variance and standard deviation for the lifetimes of inexpensive wristwatches if a sample of 24 watches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Do you feel that the lifetimes are relatively consistent?
The number of carbohydrates (in grams) per 8-ounce serving of yogurt for each of a random selection of brands is listed below. Estimate the true population variance and standard deviation for the number of carbohydrates per 8-ounce serving of yogurt with 95% confidence.17
A study of generation related carbon monoxide deaths showed that a sample of 6 recent years had a standard deviation of 4.1 deaths per year. Find the 99% confidence interval of the variance and standard distribution. Assume the variable is normally distributed.
U.S. insurers’ costs for knee replacement surgery range from $17,627 to $25,462. Estimate the population variance (standard deviation) in cost with 98% confidence based on a random sample of 10 persons who have had this surgery. The retail costs (for uninsured persons) for the same procedure
Find the 90% confidence interval for the variance and standard deviation of the ages of seniors at Oak Park College if a sample of 24 students has a standard deviation of 2.3 years .Assume the variable is normally distributed.
A new-car dealer is leasing various brand-new models for the monthly rates (in dollars) listed below. Estimate the true population variance (and standard deviation) in leasing rates with 90% confidence.169 169 199 239 239 249
In each case, p̂ find an q̂.a. n = 80 and X = 40 b. n = 200 and X = 90c. n = 130 and X = 60d. n = 60 and X = 35e. n = 95 and X = 43
In a sample of 200 people, 154 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence
A nutritionist found that in a sample of 80 families, 25% indicated that they ate fruit at least 3 times a week. Find the 99% confidence interval of the true proportion of families who said that they ate fruit at least 3 times a week. Would a proportion of families equal to 28% be considered large?
It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 400 incoming college freshmen was asked their preference, and 95 replied that they were considering business as a major. Estimate the true proportion of freshman
In a Gallup Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the 95% confidence interval for the true proportion of individuals who feel they are worse off financially.
In a poll of 1000 likely voters, 5 60 say that the United States spends too little on fighting hunger at home. Find a 95% confidence interval for the true proportion of voters who feel this way.
A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 4% of the true proportion. Find the sample necessary if in a prior study, a sample of 200 people showed that 40 traveled overseas last year. If no estimate of the sample
A recent study indicated that 29% of the 100 women over age 55 in the study were widows.a. How large a sample must you take to be 90% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows? b. If no estimate of the sample proportion is available,
It is believed that 25% of U.S. homes have a direct satellite television receiver. How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points? How large a sample is necessary if nothing is known about the proportion?
Obesity is defined as a body mass index (BMI) of 30 kg/m2 or more. A 95% confidence interval for the percentage of U.S. adults aged 20 years and over who were obese was found to be 22.4 to 23.5%. What was the sample size?
Nearly one-half of Americans aged 25 to 29 are unmarried. How large a sample is necessary to estimate the true proportion of unmarried Americans in this age group within 21⁄2 percentage points with 90% confidence?
Find p̂ and q̂ for each percentage. (Use each percentage for .)a. 25%b. 42%c. 68%d. 55%e. 12%
A federal report indicated that 27% of children ages 2 to 5 years had a good diet—an increase over previous years. How large a sample is needed to estimate the true proportion of children with good diets within 2% with 95% confidence?
If a sample of 600 people is selected and the researcher decides to have a margin of error of 4% on the specific proportion who favor gun control, find the degree of confidence. A recent study showed that 50% were in favor of some form of gun control.
In a study, 68% of 1015 adults said that they believe the Republicans favor the rich. If the margin of error was 3 percentage points, what was the confidence interval used for the proportion?

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