In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that (a) exactly 250 of those surveyed feel the state of morals is poor. (b) no more than 220 of those surveyed feel the state of morals is poor. (c) more than 250 of those surveyed feel the state of morals is poor. (d) between 220 and 250, inclusive, believe the state of morals is poor. (e) at least 260 adult Americans believe the overall state of moral values is poor. Would you find this result unusual? Why?
> Number on a football player’s jersey
> Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with = 100 and = 15. Explain your reasoning. (a) /for a random sample of size n = 10. (b) /for a random sampl
> We assume that we are obtaining simple random samples from infinite populations when obtaining sampling distributions. If the size of the population is finite, we technically need a finite population correction factor. However, if the sample size is smal
> State the Central Limit Theorem.
> Explain what a sampling distribution is.
> In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, . . . , 36. (See the photo.) To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball fal
> Bicycle sharing exists in a variety of cities around the country. Los Angeles has the Metro Bike Share system. Users pick up a bike from one station, go for a ride, and return the bike to any station. Go to www.pearsonhighered.com/sullivanstats and downl
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Draw a relative histogram of the variable “Length.” Describe the shape o
> The following data represent the running lengths (in minutes) of the winners of the Academy Award for Best Picture for the years 2012–2017. (a) Compute the population mean, . (b) List all possible samples with size n = 2. There should be 6C2 = 15 sample
> The following data represent the ages of the winners of the Academy Award for Best Actor for the years 2012–2017. (a) Compute the population mean, . (b) List all possible samples with size n = 2. There should be 6C2 = 15 samples. (c) Construct a samplin
> According to Crown ATM Network, the mean ATM withdrawal is $67. Assume that the standard deviation for withdrawals is $35. (a) Do you think the variable “ATM withdrawal” is normally distributed? If not, what shape would you expect the variable to have? (
> A salesperson obtained a systematic sample of size 20 from a list of 500 clients. To do so, he randomly selected a number from 1 to 25, obtaining the number 16. He included in the sample the 16th client on the list and every 25th client thereafter. List
> The amount of time Americans spend watching television is closely monitored by firms such as AC Nielsen because this helps determine advertising pricing for commercials. (a) Do you think the variable “weekly time spent watching television” would be norma
> Suppose that cars arrive at Burger King’s drive-thru at the rate of 20 cars every hour between 12:00 noon and 1:00 P.M. A random sample of 40 one- hour time periods between 12:00 noon and 1:00 P.M. is selected and has 22.1 as the mean number of cars arri
> The Food and Drug Administration sets Food Defect Action Levels (FDALs) for some of the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL for insect filth in peanut butter is 3 insect fragmen
> The quality-control manager of a Long John Silver’s restaurant wants to analyze the length of time that a car spends at the drive-thru window waiting for an order. It is determined that the mean time spent at the window is 59.3 seconds with a standard de
> The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is skewed right. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-change time is
> A very good poker player is expected to earn $1 per hand in $100/$200 Texas Hold’em. The standard deviation is approximately $32. (a) What is the probability a very good poker player earns a profit (more than $0) after playing 50 hands in $100/$200 Texas
> The S&P 500 is a collection of 500 stocks of publicly traded companies. Using data obtained from Yahoo! Finance, the monthly rates of return of the S&P 500 since 1950 are approximately normal. The mean rate of return is 0.007233 (0.7233%), and the standa
> The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is approximately normal with standard deviation 21.25 minutes, answer the following
> The reading speed of second-grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. (a) What is the probability a randomly selected student will read more than 95 words per minute? (b) What is
> The upper leg length of 20- to 29-year-old males is approximately normal with a mean length of 43.7 cm and a standard deviation of 4.2 cm. Source: “Anthropometric Reference Data for Children and Adults: U.S. Population, 1999–2002”; Volume 361, July 7, 20
> 24 Hour Fitness wants to administer a satisfaction survey to its current members. Using its membership roster, the club randomly selects 40 club members and asks them about their level of satisfaction with the club.
> The length of human pregnancies is approximately normal with mean = 266 days and standard deviation = 16 days. (a) What is the probability a randomly selected pregnancy lasts less than 260 days? (b) Suppose a random sample of 20 pregnancies is obtain
> A simple random sample of size n = 20 is obtained from a population with = 64 and = 17. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming t
> A simple random sample of size n = 12 is obtained from a population with = 64 and = 17. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming t
> A simple random sample of size n = 36 is obtained from a population with = 64 and = 18. (a) Describe the sampling distribution of /. (b) What is / (c) What is / (d) What is /
> A simple random sample of size n = 49 is obtained from a population with / (a) Describe the sampling distribution of /. (b) What is / (c) What is / (d) What is /
> Answer the following questions for the sampling distribution of the sample mean shown to the right. (a) What is the value of / (b) What is the value of / (c) If the sample size is n = 9,what is likely true about the shape of the population? (d) If the
> Answer the following questions for the sampling distribution of the sample mean shown to the right. (a) What is the value of / (b) What is the value of / (c) If the sample size is n = 16, what is likely true about the shape of the population? (d) If the
> = 27, = 6, n = 15
> = 52, = 10, n = 21
> = 64, = 18, n = 36
> To determine his DSL Internet connection speed, Shawn divides up the day into four parts: morning, midday, evening, and late night. He then measures his Internet connection speed at 5 randomly selected times during each part of the day.
> = 80 = 14, n = 49
> A simple random sample of size n = 40 is obtained from a population with = 50 and = 4. Does the population need to be normally distributed for the sampling distribution of / to be approximately normally distributed? Why? What is the sampling distribu
> A simple random sample of size n = 10 is obtained from a population that is normally distributed with = 30 and = 8. What is the sampling distribution of /?
> True or False: To cut the standard error of the mean in half, the sample size must be doubled.
> True or False: The distribution of the sample mean, /, will be approximately normally distributed if the sample is obtained from a population that is not normally distributed, regardless of the sample size.
> Suppose X is a binomial random variable. To approximate /
> When adding or subtracting 0.5 from x, we are making a correction for_____.
> In a binomial experiment with n trials and probability of success p, if_____ , the binomial random variable X is approximately normal with /
> According to a USA Today “Snapshot,” 3% of Americans surveyed lie frequently. You conduct a survey of 500 college students and find that 20 of them lie frequently. (a) Compute the probability that, in a random sample of 500 college students, at least 20
> In a Pew Research poll, 42% of adult Americans had a positive view of socialism. You conduct a survey of 200 randomly selected students at your school and find that 103 have a positive view of socialism. (a) Approximate the probability that, in a random
> The presider of a guest-lecture series at a university stands outside the auditorium before a lecture begins and hands every fifth person who arrives, beginning with the third, a speaker evaluation survey to be completed and returned at the end of the pr
> According to the Current Population Survey (Internet release date: September 15, 2004), 46% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home.) Suppose a surve
> According to the Current Population Survey (Internet release date: September 15, 2004), 55% of males between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home.) Suppose a survey
> According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individ
> In the Healthy Handwashing Survey conducted by Bradley Corporation, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose you survey a random sample of 740 adult American women aged 18–24 yea
> According to American Airlines, Flight 215 from Orlando to Los Angeles is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to (a) approximate the probability that exactly 130 flights are on time. (b) a
> n = 85, p = 0.8, x = 70
> n = 75, p = 0.75, x = 60
> n = 100, p = 0.05, x = 50
> n = 40, p = 0.25, x = 30
> A survey regarding download time on a certain website is administered on the Internet by a market research firm to anyone who would like to take it.
> n = 80, p = 0.15, x = 18
> n = 60, p = 0.4, x = 20
> The probability that fewer than 35 people support the privatization of Social Security
> The probability that no more than 500 adult Americans support a bill proposing to extend daylight savings time
> The probability that fewer than 40 households have a pet
> The probability that more than 20 people want to see the marriage tax penalty abolished
> The probability that the number of tornadoes that occur in the month of May is between 30 and 40, inclusive
> The probability that the number of people with blood type O-negative is between 18 and 24, inclusive
> The probability that exactly 12 students pass the course
> The probability that exactly eight defective parts are in the shipment
> A college official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a simple random sample from each class and asks the members’ opinions regarding student services.
> The probability no more than 20 people want to see Roe v. Wade overturned
> The probability that at least 40 households have a gas stove
> Suppose X is a binomial random variable. To approximate /
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> True or False: A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal.
> A_____ ____ ______ is a graph that plots observed data versus normal scores.
> Retrieve the data 7_3_13 at www.pearsonhighered.com/sullivanstats using the file format of your choice for the text you are using. The data represent the time spent waiting in line (in minutes) for the Dinosaur Ride at Walt Disney World for 100 randomly
> A random sample of college students aged 18–24 years was obtained, and the number of hours of television watched in a typical week was recorded. (a) Draw a normal probability plot to determine if the data could have come from a normal distribution. (b) D
> A farmer divides his orchard into 50 subsections, randomly selects 4, and samples all the trees within the 4 subsections to approximate the yield of his orchard.
> In a 1998 advertising campaign, Nabisco claimed that every 18-ounce bag of Chips Ahoy! cookies contained at least 1000 chocolate chips. Brad Warner and Jim Rutledge tried to verify the claim. The following data represent the number of chips in an 18-ounc
> A random sample of 25 years between 1890 and 2018 was obtained, and the amount of snowfall, in inches, for Memphis was recorded.
> A random sample of 20 undergraduate students receiving student loans was obtained, and the amount of their loans for the 2018–2019 school year was recorded.
> A random sample of weekly work logs at an automobile repair station was obtained, and the average number of customers per day was recorded.
> A random sample of O-rings was obtained, and the wall thickness (in inches) of each was recorded.
>
> Determine the area under the standard normal curve that lies to the left of (a) z = -2.45 (b) z = -0.43 (c) z = 1.35 (d) z = 3.49
> If X is normal random variable with mean 40 and standard deviation 10 and P(X < 38) = 0.4207, then P(X ≤ 38) =____.
> If X is a normal random variable with mean 40 and standard deviation 10 and P(X >45) = 0.3085, then P(X < 35) =_____.
> The notation za is the z-score such that the area under the standard normal curve to the right of za is______.
> A radio station asks its listeners to call in their opinion regarding the use of U.S. forces in peacekeeping missions.
> A random variable Z that is normally distributed with mean = 0 and standard deviation = 1 is said to have the _____ ______.
> The ACT and SAT are two college entrance exams. The composite score on the ACT is approximately normally distributed with mean 21.1 and standard deviation 5.1. The composite score on the SAT is approximately normally distributed with mean 1026 and standa
> Explain why P(X ≤220) should be reported as > 0.9999 if X is a normal random variable with mean 100 and standard deviation 15.
> Explain why P(X < 30) should be reported as
> Give three interpretations for the area under a normal curve.
> The file 7_2_53 represents distance (in feet) of all home runs hit during the 2018 Major League baseball season. It is available at www.pearsonhighered.com/sullivanstats. (a) Draw a relative frequency histogram of the home run distances using a lower cla
> The following data represent the distribution of birth weights (in grams) for babies in which the pregnancy went full term (37–41 weeks). (a) Construct a relative frequency distribution for birth weight. (b) Draw a relative frequency histogram for birth
> The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. (a) Speedy Lube guarantees customers that the service wil
> Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-thru. Certainly, the faster the cars get through the drive-thru, the more the opportunity for making money. QSR Magazine studied drive-thru times for fa
> The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the U.S. Air Force Academy. S
> In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product.
> The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile? (
