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elementary statistics

Elementary Statistics 3rd Edition William Navidi, Barry Monk - Solutions

If a normal population has a mean of μ and a standard deviation of σ, then the area to the left of μ is less than 0.5.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If a normal population has a mean of ???? and a standard deviation of σ, then the area to the right of μ + σ is less than 0.5.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If a normal population has a mean of μ and a standard deviation of σ, then P(X = μ) = 1.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If a normal population has a mean of μ and a standard deviation of σ, then P(X = μ) = 0.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
A normal population has mean μ = 20 and standard deviationσ = 4.a. What proportion of the population is less than 18?b. What is the probability that a randomly chosen value will be greater than 25?
A normal population has mean μ = 9 and standard deviationσ = 6.a. What proportion of the population is less than 20?b. What is the probability that a randomly chosen value will be greater than 5?
A normal population has mean μ = 25 and standard deviationσ = 11.a. What proportion of the population is greater than 34?b. What is the probability that a randomly chosen value will be less than 10?
A normal population has mean μ = 61 and standard deviationσ = 16.a. What proportion of the population is greater than 100?b. What is the probability that a randomly chosen value will be less than 80?
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 and 55?
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 and 40?
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 baby to weigh more than 17 pounds?
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 2.7 pounds.a. What proportion of babies weigh more than 13 pounds?b. What proportion of babies weigh
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 9.9.a. Find the 30th percentile of the blood pressures.b. Find the 67th percentile of the blood
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 weights.b. Find the 10th percentile of the baby weights.c. Find the first quartile of the baby weights.
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 millimeters. Assume these lengths are normally distributed.a. What proportion of six-year-old rainbow trout are
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 of broilers weigh between 1100 and 1200 grams?b. What is the probability that a randomly selected
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 these lengths are normally distributed.a. Find the 58th percentile of the lengths.b. Find the 76th
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 the 22nd percentile of the weights.b. Find the 93rd percentile of the weights.c. Find the first
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 be dangerous. A radon level less than 4.0 picocuries is considered safe. Because levels fluctuate
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 standard deviation$20.00.a. What proportion of bills are greater than $130?b. What proportion of
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 measurements.c. Find the median of the measurements.
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 standard deviation $20.00.a. Find the 7th percentile of the bill amounts.b. Find the 62nd percentile of
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 tire has a lifetime greater than 48 thousand miles?b. What proportion of tires have lifetimes between
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 tall?b. What proportion of trees are less than 100 inches tall?c. What is the probability that a randomly
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. Find the 68th percentile of the tire lifetimes.c. Find the first quartile of the tire lifetimes.d.
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 85th percentile of the tree heights.c. Find the third quartile of the tree heights.d. An
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 than 12.06 ounces?b. What is the probability that a randomly selected can will contain between 12 and
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 proportion of students studied more than 40 hours?b. What is the probability that a randomly selected
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 volumes.c. Between what two values are the middle 95% of the volumes?
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 98th percentile of the number of hours studying.b. Find the 32nd percentile of the number of hours
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 25.0 millimeters?b. What proportion of the diameters are greater than 25.4 millimeters?c. To meet a
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 were below 65?c. What is the probability that a randomly chosen score is between 70 and 80?
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. Find the 32nd percentile of the diameters.c. A hole is to be designed so that 1% of the ball bearings
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 scores.c. The instructor wants to give an A to the students whose scores were in the top 10% 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 determine whether these concentrations are approximately normally distributed?If so, say whether
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 selected at random, what is the probability that at least one of them is more than 68 inches tall?
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 work so that the probability she is on time is 95%?
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? Explain.
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 48? Explain.
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 the statement is true or false. If the statement is false, rewrite it as a true statement. n
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 it as a true statement.
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 probability that ̄x will be greater than 4.c. If appropriate find the 30th percentile of x̄.
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 probability that x̄ will be between 53 and 54.c. If appropriate find the 45th percentile of x̄.
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 find the probability that ̄x will be between 50 and 70.c. If appropriate find the 80th percentile of
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 the probability that x̄ will be less than 120.c. If appropriate find the 90th percentile of x̄.
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. List all samples of size 2 drawn with replacement. There are 5 × 5 = 25 different samples.c. Compute
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 of Benjamin Haggerty (Macklemore). Ages are given to the nearest half year so the five ages are all
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 company buys 60 of these cars.a. What is the probability that the average mileage of the fleet is
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 milligrams per deciliter). A simple random sample of 110 adults is chosen.a. What is the probability
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 sample mean number of TV sets is greater than 2?b. What is the probability that the sample mean
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 mean score is less than 500?b. What is the probability that the sample mean score is between 480 and
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 to study the effect of a new tax law.a. What is the probability that the sample mean tax is less
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 apartments.a. What is the probability that the sample mean rent is greater than $2700?b. What is the
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 of adult U.S. men have mean 194 pounds and standard deviation 68 pounds, and the weights of adult
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 weights of adult U.S.men have mean 194 pounds and standard deviation 68 pounds, and the weights of adult
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 that the sample mean income is less than 38?b. What is the probability that the sample mean income is
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 chosen.a. What is the probability that the sample mean commute distance is greater than 13 miles?b. What 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 randomly chosen page is more than 0.1 mm thick. Is enough information given to compute this
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 that a randomly chosen bag weighs more than 10 pounds. Is enough information given to compute this
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 ̄x denote the mean weight of the 75 boxes.a. If the claim is true, what is P(̄ x̄ ≤ 11.99)?b.
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 batteries in a simple random sample of size 100.a. If the claim is true, what is P( x̄ ≤
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 multiplying by a correction factor. Specifically, if the sample size is more than 5% of the population
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 saw a doctor?b. Would it be unusual if more than 70% of them saw a doctor?
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 defective chips in the shipment is between 0.08 and 0.15?b. Would it be unusual for 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 appropriate word or phrase.
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 true statement.
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 false, rewrite it as a true statement.
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 indicated probability.
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 indicated probability.
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 indicated probability.
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 find the indicated probability.
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 find the indicated probability.
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 find the indicated probability.
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 the probability that more than 67% of the sampled adults drink coffee daily.d. Find the probability
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 probability that more than 70% of the sampled teenagers own a smartphone.d. Find the probability that
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 μp̂.b. Find the standard deviation σp̂.c. Find the probability that less than 60% of the people in the
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 chosen.a. Find the mean μp̂.b. Find the standard deviation σp̂c. Find the probability that less
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 probability that less than 20% of the individuals in the sample are government employees? If so,
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 use the normal approximation to find the probability that less than 6.5% of the individuals in the
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 have expressed interest in a STEM discipline. A random sample of 85 freshmen is selected.a. Is it
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 blood pressure is 0.3. A sample of 38 U.S. adults is chosen.a. Is it appropriate to use the normal
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 tax returns.a. What is the probability that the sample proportion of tax returns for which no tax
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 earnings of more than $837?b. A sample of 150 full-time employees is chosen. What is the probability that

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