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elementary statistics

Questions and Answers of Elementary Statistics

A normal population has mean μ = 47 and standard deviationσ = 3.a. What proportion of the population is between 40 and 50?b. What is the probability that a randomly chosen value will be between 50
A normal population has mean μ = 35 and standard deviationσ = 8.a. What proportion of the population is between 20 and 30?b. What is the probability that a randomly chosen value will be between 30
A normal population has mean μ = 12 and standard deviation σ = 3.What is the 40th percentile of the population?
A normal population has mean μ = 56 and standard deviation σ = 8.What is the 85th percentile of the population?
A normal population has mean μ = 46 and standard deviation σ = 9.What is the 19th percentile of the population?
A normal population has mean μ = 71 and standard deviation σ = 33.What is the 91st percentile of the population?c. What proportion of babies weigh between 10 and 14 pounds?d. Is it unusual for a
According to a recent National Health Statistics Reports, the weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation
The Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.5 and standard deviation
The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds.a. Find the 81st percentile of the baby
According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41
According to thepoultrysite.com, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams.a. What proportion
The U.S. Fish and Wildlife Service reported that the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume
A report on thepoultrysite.com stated that the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams.a. Find
Radon is a naturally occurring radioactive substance that is found in the ground underneath many homes. Radon detectors are often placed in homes to determine whether radon levels are high enough to
According to the U.S. Energy Information Administration, the mean monthly household electric bill in the United States in a recent year was $110.14. Assume the amounts are normally distributed with
Assume that radon measurements are normally distributed with mean 4.1 picocuries and standard deviation of 0.2.a. Find the 35th percentile of the measurements.b. Find the 92nd percentile of the
The U.S. Energy Information Agency reported that the mean monthly household electric bill in the United States in a recent year was \($110.14\). Assume the amounts are normally distributed with
The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ = 40 and standard deviation σ = 5.a. What is the probability that a randomly chosen
Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 112 inches and standard deviation σ = 14 inches.a. What proportion of trees are more than 120 inches
The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ = 40 and standard deviation σ = 5.a. Find the 15th percentile of the tire lifetimes.b.
Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 112 inches and standard deviation σ = 14 inches.a. Find the 27th percentile of the tree heights.b. Find
The volume of beverage in a 12-ounce can is normally distributed with mean 12.05 ounces and standard deviation 0.02 ounce.a. What is the probability that a randomly selected can will contain more
A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 7.a. What
The volume of beverage in a 12-ounce can is normally distributed with mean 12.05 ounces and standard deviation 0.02 ounce.a. Find the 60th percentile of the volumes.b. Find the 4th percentile of the
A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 7.a. Find the
A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 millimeters and standard deviation 0.08 millimeter.a. What proportion of the diameters are less than
Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.a. What proportion of the scores were above 90?b. What proportion of the scores
A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 millimeters and standard deviation 0.08 millimeter.a. Find the 60th percentile of the diameters.b.
Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.a. Find the 40th percentile of the scores.b. Find the 65th percentile of the
Heights of men in a certain city are normally distributed with mean 70 inches. Sixteen percent of the men are more than 73 inches tall. What percentage of the men are between 67 and 70 inches tall?
A study reported that the mean concentration of ammonium in water wells in the state of Iowa was 0.71 milligram per liter, and the standard deviation was 1.09 milligrams per liter. Is it possible to
According to the National Health Statistics Reports, heights of adult women in the United States are normally distributed with mean 64 inches and standard deviation 4 inches. If three women are
Megan drives to work each morning. Her commute time is normally distributed with mean 30 minutes and standard deviation 4 minutes. Her workday begins at 9:00 A.M. At what time should she leave for
A population has mean μ = 6 and standard deviation σ = 4.Find μx̄ and σ x̄ for samples of size n = 25.
A population has mean μ = 17 and standard deviation σ = 20.Find μx̄ and σ x̄ for samples of size n = 100.
A population has mean ???? = 10 and standard deviation ???? = 8.A sample of size 50 is drawn.a. Find the probability that x̄ is greater than 11.b. Would it be unusual for x̄ to be less than 8?
A population has mean μ = 47.5 and standard deviation σ = 12.6. A sample of size 112 is drawn.a. Find the probability that x̄ is between 45 and 48.b. Would it be unusual for x̄ to be greater than
The probability distribution of x̄ is called a _________________ distribution.In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
The ____________________ states that the sampling distribution of x̄ is approximately normal when the sample is large.In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
If x̄ is the mean of a large (n > 30) simple random sample from a population with mean μ and standard deviation σ, then x̄ is approximately normal withIn Exercises 7 and 8, determine whether
As the sample size increases, the sampling distribution of x̄ becomes more and more skewed.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite
A sample of size 75 will be drawn from a population with mean 10 and standard deviation 12.a. Find the probability that ̄x will be between 8 and 14.b. Find the 15th percentile of x̄.
A sample of size 126 will be drawn from a population with mean 26 and standard deviation 3.a. Find the probability that x̄ will be between 25 and 27.b. Find the 55th percentile of x̄.
A sample of size 68 will be drawn from a population with mean 92 and standard deviation 24.a. Find the probability that x̄ will be greater than 90.b. Find the 90th percentile of x̄.
A sample of size 284 will be drawn from a population with mean 45 and standard deviation 7.a. Find the probability that x̄ will be greater than 46.b. Find the 75th percentile of x̄.
A sample of size 91 will be drawn from a population with mean 33 and standard deviation 17.a. Find the probability that x̄ will be less than 30.b. Find the 25th percentile of x̄.
A sample of size 82 will be drawn from a population with mean 24 and standard deviation 9.a. Find the probability that x̄ will be less than 26.b. Find the 10th percentile of x̄.
A sample of size 20 will be drawn from a population with mean 6 and standard deviation 3.a. Is it appropriate to use the normal distribution to find probabilities for x̄?b. If appropriate find the
A sample of size 42 will be drawn from a population with mean 52 and standard deviation 9.a. Is it appropriate to use the normal distribution to find probabilities for x̄?b. If appropriate find the
A sample of size 5 will be drawn from a normal population with mean 60 and standard deviation 12.a. Is it appropriate to use the normal distribution to find probabilities for x̄?b. If appropriate
A sample of size 15 will be drawn from a population with mean 125 and standard deviation 28.a. Is it appropriate to use the normal distribution to find probabilities for x̄?b. If appropriate find
Following are the temperatures, in degrees Fahrenheit, in Denver for five days in July:a. Consider this to be a population. Find the population mean ????and the population standard deviation σ.b.
Following are the ages of the Grammy award winners for Best New Artist for the years 2013–2017.(For Fun., the age is that of guitarist Andrew Dost. For Macklemore & Ryan Lewis the age is that
The Environmental Protection Agency(EPA) rates the mean highway gas mileage of the 2017 Chevrolet Sonic to be 28 miles per gallon. Assume the standard deviation is 3 miles per gallon. A rental car
The National Health and Nutrition Examination Survey (NHANES) reported that in a recent year, the mean serum cholesterol level for U.S.adults was 202, with a standard deviation of 41 (the units are
A Nielsen Company report states that the mean number of TV sets in a U.S. household is 2.24. Assume the standard deviation is 1.2. A sample of 85 households is drawn.a. What is the probability that
The College Board reports that in a recent year, the mean mathematics SAT score was 514, and the standard deviation was 118.A sample of 65 scores is chosen.a. What is the probability that the sample
The Internal Revenue Service reports that the mean federal income tax paid in a recent year was $8040. Assume that the standard deviation is $5000. The IRS plans to draw a sample of 1000 tax returns
The Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2631. Assume the standard deviation is $500. A real estate firm samples 100
A roller coaster is being designed that will accommodate 60 riders. The maximum weight the coaster can hold safely is 12,000 pounds. According to the National Health Statistics Reports, the weights
Engineers are designing a large elevator that will accommodate 40 people. The maximum weight the elevator can hold safely is 8120 pounds. According to the National Health Statistics Reports, the
The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 30.A pollster draws a sample of 90 people to interview.a. What is the probability
An ABC News report stated that the mean distance that commuters in the United States travel each way to work is 16 miles. Assume the standard deviation is 8 miles.A sample of 75 commuters is
A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm. Someone wants to know the probability that a
A supermarket sells apples in bags labeled as weighing 10 pounds. A sample of 50 bags had a mean weight of 10.3 pounds with a standard deviation of 0.1 pound. Someone wants to know the probability
A cereal manufacturer claims that the weight of a box of cereal labeled as weighing 12 ounces has a mean of 12.0 ounces and a standard deviation of 0.1 ounce. You sample 75 boxes and weigh them. Let
A battery manufacturer claims that the lifetime of a certain type of battery has a population mean of μ = 40 hours and a standard deviation of σ = 5 hours. Let ̄x represent the mean lifetime of
The mean of a sample of size n has standard deviation σ∕√n, where ???? is the population standard deviation. When sampling without replacement, a more accurate expression can be obtained by
Find μp̂ and σp̂ if n = 20 and p = 0.82.
Find μp̂ and σp̂ if n = 217 and p = 0.455.
The General Social Survey reported that 56% of American adults saw a doctor for an illness during the past year. A sample of 65 adults is drawn.a. What is the probability that more than 60% of them
For a certain type of computer chip, the proportion of chips that are defective is 0.10.A computer manufacturer receives a shipment of 200 chips.a. What is the probability that the proportion of
If n is the sample size and x is the number in the sample who have a certain characteristic, then x∕n is called the sample ___________________ .In Exercises 5 and 6, fill in each blank with the
The probability distribution of p̂ is called a ______________________ distribution.In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
The distribution of p̂ is approximately normal if np ≥ 10 and n(1 − p) ≥ 10.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a
If n is the sample size, p is the population proportion, and p̂ is the sample proportion, then σp̂ = np.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is
n = 147, p = 0.13; P(p̂ < 0.11)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to find the
n = 65, p = 0.86; P(p̂ < 0.80)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to find the
n = 270, p = 0.57; P(p̂ > 0.61)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to find the
n = 103, p = 0.24; P(0.20 < p̂ < 0.23)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to
n = 145, p = 0.05; P(0.03 < p̂ < 0.08)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to
n = 234, p = 0.75; P(0.77 < p̂ < 0.81)In Exercises 9–14, n is the sample size, p is the population proportion, and p̂ is the sample proportion. If appropriate, use the Central Limit Theorem to
The National Coffee Association reported that 63% of U.S. adults drink coffee daily. A random sample of 250 U.S. adults is selected.a. Find the mean μp̂.b. Find the standard deviation σp̂.c. Find
A Pew Research report indicated that 73% of teenagers aged 13–17 own smartphones. A random sample of 150 teenagers is drawn.a. Find the mean μp̂.b. Find the standard deviation σp̂.c. Find the
The Institute for College Access and Success reported that 68% of college students in a recent year graduated with student loan debt. A random sample of 85 graduates is drawn.a. Find the mean
The National Center for Educational Statistics reported that 82% of freshmen entering public high schools in the U.S. in 2009 graduated with their class in 2013.A random sample of 135 freshmen is
The Bureau of Labor Statistics reported that 16% of U.S. nonfarm workers are government employees. A random sample of 50 workers is drawn.a. Is it appropriate to use the normal approximation to find
The Bureau of Labor Statistics reported in a recent year that 5% of employed adults in the United States held multiple jobs. A random sample of 75 employed adults is chosen.a. Is it appropriate to
Education professionals refer to science, technology, engineering and mathematics as the STEM disciplines. A recent ACT Condition and Career Readiness Report states that 47% of high school graduates
High blood pressure has been identified as a risk factor for heart attacks and strokes. The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high
According to the Internal Revenue Service, the proportion of federal tax returns for which no tax was paid was p = 0.326. As part of a tax audit, tax officials draw a simple random sample of n = 120
The Bureau of Labor Statistics reported that in 2016, the median weekly earnings for people employed full time in the United States was $837.a. What proportion of full-time employees had weekly
The Health Resources and Services Administration reported that 5% of people who received kidney transplants were under the age of 18.How large a sample of kidney transplant patients needs to be drawn
The General Social Survey reported that 91% of people who bought a car in the past five years were satisfied with their purchase. How large a sample of car buyers needs to be drawn so that the sample
There are two hospitals in a town. Hospital A has 200 births per month, and Hospital B has 50.a. At which hospital is it more likely that 55% or more of the births will be boys?b. At which hospital
There are two elementary schools in a town.School A has 500 students, and school B has 1000 students.a. At which school is it more likely that 55% or more of the students will be girls?b. At which
A new process has been designed to make ceramic tiles. The goal is to have no more than 5% of the tiles be nonconforming due to surface defects. A random sample of 1000 tiles is inspected. Let p̂ be
X is a binomial random variable with n = 50 and p = 0.15. Should the normal approximation be used to find P(X > 10)? Why or why not?
X is a binomial random variable with n = 72 and p = 0.90. Should the normal approximation be used to find P(X ≤ 60)? Why or why not?
Let X have a binomial distribution with n = 64 and p = 0.41. If appropriate, use the normal approximation to find P(X ≤ 20). If not, explain why not.

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