Questions and Answers of Practice of Statistics

Continuous random variables A, B, and C all take values between 0 and 10. Their density curves, drawn on the same horizontal scales, are shown here. Rank the standard deviations of the three random
From a large group of people who signed a card saying they intended to quit smoking, 1000 people were selected at random. It turned out that 210 (21%) of these individuals had not smoked over the
How much do prices vary for filling a cavity? To find out, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure at
Each month, the Current Population Survey interviews about 60,000 randomly selected U.S. adults. One of their goals is to estimate the national unemployment rate. In October 2016, 4.9% of those
To collect information such as passwords, online criminals use “spoofing” to direct Internet users to fraudulent websites. In one study of Internet fraud, students were warned about spoofing and
If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?a. 0.25b. 1.00c.d.e. (0.75)3(0.75)1A fast-food restaurant runs a promotion in which certain food items come with game
Each entry in a table of random digits like Table D has probability 0.1 of being a 0, and the digits are independent of one another. Each line of Table D contains 40 random digits. The mean and
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?a. n = 10, p =
If Jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times?a. (0.25)5b. (0.75)4c. (0.75)5d. (0.75)4(0.25)e.A fast-food restaurant runs a
Marti decides to keep placing a $1 bet on number 15 in consecutive spins of a roulette wheel until she wins. On any spin, there’s a 1-in-38 chance that the ball will land in the 15 slot.a. How many
Joe reads that 1 out of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. If eggs do or don’t contain salmonella independently of each other, the number of
According to Benford’s law (Exercise 15), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices
Determine whether each of the following scenarios describes a geometric setting. If so, define an appropriate geometric random variable.a. Shuffle a standard deck of playing cards well. Then turn
Determine whether each of the following scenarios describes a geometric setting. If so, define an appropriate geometric random variable.a. A popular brand of cereal puts a card bearing the image of 1
To start her old lawn mower, Rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20% chance of starting.a. Find the probability that it takes her exactly 3 pulls
To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than 10% of the population size N?
Alan decides to use a different strategy for the 1-in-6 wins game of Exercise 90. He keeps buying one 20-ounce bottle of the soda at a time until he gets a winner.a. Find the probability that he buys
Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both np and n(1 − p) be at least 10?
Refer to Exercise 100.a. Justify why D can be approximated by a Normal distribution.b. Use a Normal distribution to estimate the probability that 30 or more adults in the sample have more debt than
In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses her 7 tiles and is
According to financial records, 24% of U.S. adults have more debt on their credit cards than they have money in their savings accounts. Suppose that we take a random sample of 100 U.S. adults. Let D
A total of 11% of students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records L = the number of left-handed students in the sample.a.
Refer to Exercise 99.a. Justify why L can be approximated by a Normal distribution.b. Use a Normal distribution to estimate the probability that 15 or more students in the sample are
A federal report finds that lie detector tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive.11 A company asks 12 job applicants about thefts from previous
The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such
When a polling company calls a telephone number at random, there is only a 9% chance that the call reaches a live person and the survey is successfully completed.10 Suppose the random digit dialing
An online spinner has two colored regions—blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is
Refer to Exercise 92.a. Calculate and interpret the mean of T.b. Calculate and interpret the standard deviation of T.Exercise 92.A company has developed an “easy-start” mower that cranks the
Refer to Exercise 91.a. Calculate and interpret the mean of R.b. Calculate and interpret the standard deviation of R.Exercise 91.Thousands of travelers pass through the airport in Guadalajara,
Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must go through the customs inspection area. Customs agents want to be
As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each bottle cap. Some of the caps said, “Please try again!” while others said,
Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red on a
A company has developed an “easy-start” mower that cranks the engine with the push of a button. The company claims that the probability the mower will start on any push of the button is 0.9.
Refer to Exercise 84. Calculate and interpret P(Y ≥ 7).Exercise 84.An online spinner has two colored regions—blue and yellow. According to the website, the probability that the spinner lands in
Do people have a preference for the last thing they taste? Researchers at the University of Michigan designed a study to find out. The researchers gave 22 students five different Hershey’s Kisses
Refer to Exercise 83. Calculate and interpret P(X ≤ 7).Exercise 83.An online spinner has two colored regions—blue and yellow. According to the website, the probability that the spinner lands in
Refer to Exercise 80. Would you be surprised if the train arrived on time on fewer than 4 days? Calculate an appropriate probability to support your answer.Exercise 80.According to New Jersey
Refer to Exercise 77. How surprising would it be for more than 4 elk in the sample to survive to adulthood? Calculate an appropriate probability to support your answer.Exercise 77.Biologists estimate
Refer to Exercise 80. Use the binomial probability formula to find P(Y = 4). Interpret this value.Exercise 80.According to New Jersey Transit, the 8:00 A.M. weekday train from Princeton to New York
Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red on a
An online spinner has two colored regions—blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is
Refer to Exercise 77. Use the binomial probability formula to find P(X = 4). Interpret this value.Exercise 77.Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to
Lawrence likes to shoot a bow and arrow in his free time. On any shot, he has about a 10% chance of hitting the bull’s-eye. As a challenge one day, Lawrence decides to keep shooting until he gets a
Put the names of all the students in your statistics class in a hat. Mix up the names, and draw 4 without looking. Let X = the number whose last names have more than six letters.Determine whether the
According to New Jersey Transit, the 8:00 A.M. weekday train from Princeton to New York City has a 90% chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days
Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X =
In an experiment to measure the effect of fluoride “varnish” on the incidence of tooth cavities, thirty-four 10- year-old girls whose parents volunteered them for the study were randomly assigned
You purchase a hot stock for $1000. The stock either gains 30% or loses 25% each day, each with probability 0.5. Its returns on consecutive days are independent of each other. You plan to sell the
The standard deviation of T isa. 22.b. 16.c. 15.62.d. 11.66.e. 4.The number of calories in a 1-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation
The mean of T isa. 110.b. 140.c. 180.d. 195.e. 250.The number of calories in a 1-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number
Leona and Fred are friendly competitors in high school. Both are about to take the ACT college entrance examination. They agree that if one of them scores 5 or more points better than the other, the
The amount of nitrogen oxides (NOX) present in the exhaust of a particular model of old car varies from car to car according to a Normal distribution with mean 1.4 grams per mile (g/mi) and standard
Ken is traveling for his business. He has a new 0.85- ounce tube of toothpaste that’s supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes
Andrea and Barsha are middle-distance runners for their school’s track team. Andrea’s time A in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of
A time-and-motion study measures the time required for an assembly line worker to perform a repetitive task. The data show that the time X required to bring a part from a bin to its position on an
If we randomly select four insured 21-year-old men, the insurer’s average income isV = X1 + X2 + X3 + X4/4where Xi is the income from insuring one man. Assuming that the amount of
Hanover High School has the best women’s swimming team in the region. The 400-meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters.
Lamar and Hareesh run a two-person lawn-care service. They have been caring for Mr. Johnson’s very large lawn for several years, and they have found that the time L it takes Lamar to mow the lawn
The risk of insuring one person’s life is reduced if we insure many people. Suppose that we randomly select two insured 21 year-old males, and that their ages at death are independent. If X1 and X2
Refer to Exercise 50. Assume that the number of nonword errors X and word errors Y in a randomly selected essay are independent random variables. An English professor deducts 3 points from a
Refer to Exercise 49. Note that X and Y are independent random variables because the two students are randomly selected from each of the campuses. At the main campus, full-time students pay $50 per
Refer to Exercise 52.a. Assume that B and W are independent random variables. Explain what this means in context.b. Calculate and interpret the standard deviation of the difference D (Bus − Walk)
Refer to Exercise 49. Note that X and Y are independent random variables because the two students are randomly selected from each of the campuses. Calculate and interpret the standard deviation of
Refer to Exercise 51.a. Assume that F and M are independent random variables. Explain what this means in context.b. Calculate and interpret the standard deviation of the difference D = F − M in
Refer to Exercise 50. Assume that the number of nonword errors X and word errors Y in a randomly selected essay are independent random variables. Calculate and interpret the standard deviation of the
Imagine that we randomly select a day from the past 10 years. Let X be the recorded rainfall on this date at the airport in Orlando, Florida, and Y be the recorded rainfall on this date at Disney
Refer to Exercise 50. An English professor deducts 3 points from a student’s essay score for each nonword error and 2 points for each word error. Find the mean of the total score deductions T for a
Researchers randomly select a married couple in which both spouses are employed. Let X be the income of the husband and Y be the income of the wife. Suppose that you know the means μX and μY and
Sulé’s job is just a few bus stops away from his house. While it can be faster to take the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sulé
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures academic motivation and study habits. The SSHA score F of a randomly selected female student at a large
Typographical and spelling errors can be either “nonword errors” or “word errors.” A nonword error is not a real word, as when “the” is typed as “teh.” A word error is a real word,
El Dorado Community College has a main campus in the suburbs and a downtown campus. The amount X spent on tuition by a randomly selected student at the main campus has mean $732.50 and standard
a. Find the median of G.b. Find the interquartile range (IQR) of G.Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the
A company’s single-serving cereal boxes advertise 1.63 ounces of cereal. In fact, the amount of cereal X in a randomly selected box can be modeled by a Normal distribution with a mean of 1.70
During the winter months, the temperatures at the Starneses’ Colorado cabin can stay well below freezing (32°F or 0°C) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets
a. Find the mean of G.b. Find the range of G.Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the class answered
Sally takes the same bus to work every morning. Let X = the amount of time (in minutes) that she has to wait for the bus on a randomly selected day. The probability distribution of X can be modeled
How does your web browser get a file from the Internet? Your computer sends a request for the file to a web server, and the web server sends back a response. Let Y = the amount of time (in seconds)
Ana is a dedicated Skee Ball player who always rolls for the 50-point slot. Ana’s score X on a randomly selected roll of the ball has the probability distribution shown here with mean μX = 23.8
A small ferry runs every half hour from one side of a large river to the other. The number of cars X on a randomly chosen ferry trip has the probability distribution shown here with mean μX=3.87 and
Victoria parks her car at the same garage every time she goes to work. Because she stays at work for different lengths of time each day, the fee the parking garage charges on a randomly selected day
Airlines typically accept more reservations for a flight than the number of seats on the plane. Suppose that for a certain route, an airline accepts 40 reservations on a plane that carries 38
Total gross profits G on a randomly selected day at Tim’s Toys follow a distribution that is approximately Normal with mean $560 and standard deviation $185. The cost of renting and maintaining the
The time X it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean 15 minutes and standard deviation 6.5 minutes. Once he parks his
a. What is the equation of the least-squares regression line relating posttest and pretest scores? Define any variables used.b. Is a linear model appropriate for describing this relationship? Justify
a. Did students tend to have higher reading scores after participating in the chess program? Justify your answer.b. If the study found a statistically significant improvement in the average reading
A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1. If
About what percentage of households have a number of cars within 2 standard deviations of the mean?a. 68%b. 71%c. 93%d. 95%e. 98%Choose an American household at random and let the random variable X
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow an approximately Normal distribution with mean 115 miles per hour (mph) and standard deviation 6
The standard deviation of X is σX = 1.08. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?a. The mean number of cars would be
What’s the expected number of cars in a randomly selected American household?a. 1.00b. 1.75c. 1.84d. 2.00e. 2.50Choose an American household at random and let the random variable X be the number of
Machines that fill bags with powdered sugar are supposed to dispense 32 ounces of powdered sugar into each bag. Let X = the weight (in ounces) of the powdered sugar dispensed into a randomly selected
Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and
An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject
Sally takes the same bus to work every morning. Let X = the amount of time (in minutes) that she has to wait for the bus on a randomly selected day. The probability distribution of X can be modeled
A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute.7
Examine how Benford’s law (Exercise 9) can be used to detect fraud.A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts
How does your web browser get a file from the Internet? Your computer sends a request for the file to a web server, and the web server sends back a response. Let Y = the amount of time (in seconds)
a. Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first
How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San José,

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