Question: Critical reading SAT scores are distributed as

> Support for the legalization of marijuana has continued to grow among Americans. A 2017 Gallup poll found that 64% of Americans now say that marijuana use should be legal. Suppose a random sample of 150 Americans is selected. a. Find the probability that

> According to a Pew poll, 67% of Americans believe that jury duty is part of good citizenship. Suppose 500 Americans are randomly selected. a. Find the probability that more than half believe that jury duty is part of good citizenship. b. In a group of 50

> According to the Pew Research Center, 73% of Americans have read at least one book during the past year. Suppose 200 Americans are randomly selected. a. Find the probability that more than 150 have read at least one book during the past year. b. Find the

> Voice-controlled video assistants are being incorporated into a wide variety of consumer products, including smartphones, tablets, and stand-alone devices such as the Amazon Echo or Google Home. A Pew Research poll found that 46% of Americans reported us

> Ignaz Semmelweiss (1818–1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients. Before the new procedure was established, the rate of infection at Dr. Semmelweiss’s hospital was about 10%. A

> According to studies done in the 1940s, 29% of people dream in color. Assuming this is still true, find the probability that in a random sample of 200 independent people, 50% or more will report dreaming in color. Start by checking the conditions to see

> The distribution of spring high temperatures in Los Angeles is approximately Normal, with a mean of 75 degrees and a standard deviation of 2.5 degrees. a. What is the probability that the high temperature is less than 70 degrees in Los Angeles on a day i

> Systolic blood pressures are approximately Normal with a mean of 120 and a standard deviation of 8. a. What percentage of people have a systolic blood pressure above 130? b. What is the range of systolic blood pressures for the middle 60% of the populati

> A Gallup poll conducted in 2017 found that 648 out of 1011 people surveyed supported same-sex marriage. An NBC News/Wall Street Journal poll conducted the same year surveyed 1200 people and found 720 supported same-sex marriage. a. Find both sample propo

> a. From your answers in Exercise 6.7, find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks, and report the distribution in a table. b. Make a probability distribution graph of this.

> Medical school graduates who want to become doctors must pass the U.S. Medical Licensing Exam (USMLE). Scores on this exam are approximately Normal with a mean of 225 and a standard deviation of 15. Use the Empirical Rule to answer these questions. a. Ro

> In a 2018 survey conducted by Northeastern University, 28% of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a 95% confidence interval w

> According to the Bureau of Labor Statistics, 10.1% of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that

> In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, 38% responded yes. In 2018, 31% said it would be very hard to give up watching television. a. Assume that both polls

> According to a Gallup poll, 45% of Americans actively seek out organic foods when shopping. Suppose a random sample of 500 Americans is selected and the proportion who actively seek out organic foods is recorded. a. What value should we expect for the sa

> In a game of chance, players draw one cube out of a bag containing 3 red cubes, 2 white cubes, and 1 blue cube. The player wins $5 if a blue cube is drawn, the player loses $2 if a white cube is drawn. If a red cube is drawn, the player does not win or l

> Pew Research conducts polls on social media use. In 2012, 66% of those surveyed reported using Facebook. In 2018, 76% reported using Facebook. a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who rep

> A student was tested to see if he could tell the difference between two different brands of cola. He was presented with 20 samples of cola and correctly identified 12 of the samples. Since he was correct 60 percent of the time, can we conclude that he ca

> In Toronto, Canada, 55% of people pass the drivers’ road test. Suppose that every day, 100 people independently take the test. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c.

> The 2017 Chapman University Survey of American Fears asked a random sample of 1207 adults Americans if they believed that aliens had come to Earth in modern times, and 26% responded yes. a. What is the standard error for this estimate of the percentage o

> Make a list of all possible outcomes for gender when a family has two children. Assume that the probability of having a boy is 0.50 and the probability of having a girl is also 0.50. Find the probability of each outcome in your list.

> A random sample of likely voters showed that 55% planned to vote for Candidate X, with a margin of error of 2 percentage points and with a 95% confidence level. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage o

> According to a study by the Colorado Department of Transportation, 25% of Colorado drivers admit to using their cell phones to send texts while driving. Suppose two Colorado drivers are randomly selected. a. If the driver texts while driving, record a T.

> According to a report by the American Academy of Orthopedic Surgeons, 29% of pedestrians admit to texting while walking. Suppose two pedestrians are randomly selected. a. If the pedestrian texts while walking, record a T. If not, record an N. List all po

> A Gallup poll asked a random samples of Americans in 2016 and 2018 if they were satisfied with the quality of the environment. In 2016, 543 were satisfied with the quality of the environment and 440 were dissatisfied. In 2018, 461 were satisfied and 532

> A Gallup poll asked college students in 2016 and again in 2017 whether they believed the First Amendment guarantee of freedom of the press was secure or threatened in the country today. In 2016, 2489 out of 3072 students surveyed said that freedom o

> In each case, choose whether the appropriate test is a one-proportion z-test or a two-proportion z-test. Name the population(s). a. A researcher takes a random sample of 4-year-olds to find out whether girls or boys are more likely to know the alphabet.

> Give the null and alternative hypotheses for each test, and state whether a one-proportion z-test or a two-proportion z-test would be appropriate. a. You test a person to see whether he can tell tap water from bottled water. You give him 20 sips selected

> In a 2018 study reported in The Lancet, Mercie et al. investigated the efficacy and safety of varenicline for smoking cessation in people living with HIV. The study was a randomized, double-blind, placebo-controlled trial. Of the 123 subjects treated wit

> In a 2018 study reported in The Lancet, Molina et al. reported on a study for treatment of patients with HIV-1. The study was a randomized, controlled, double-blind study that compared the effectiveness of ritonavir-boosted darunavir (rbd), the drug curr

> According to a 2018 Pew Research report, 40% of Americans read print books exclusively (rather than reading some digital books). Suppose a random sample of 500 Americans is selected. a. What percentage of the sample would we expect to read print books ex

> When a certain type of thumbtack is flipped, the probability of its landing tip up (U) is 0.60 and the probability of its landing tip down (D) is 0.40. Now suppose we flip two such thumbtacks: one red, one blue. Make a list of all the possible arrangemen

> According to a 2017 Gallup poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1000 Americans is selected. a. What percentage of the sample would we expect to report being afflicted by stress? b. Verify that the conditions

> According to a 2017 Pew Research report, 40% of millennials have a BA degree. Suppose we take a random sample of 500 millennials and find the proportion who have a driver’s license. Find the probability that at most 35% of the sample has a BA degree. Beg

> According to a 2017 article in The Washington Post, 72% of high school seniors have a driver’s license. Suppose we take a random sample of 100 high school seniors and find the proportion who have a driver’s license. Find the probability that more than 75

> If we do not reject the null hypothesis, is it valid to say that we accept the null hypothesis? Why or why not?

> The null hypothesis on true/false tests is that the student is guessing, and the proportion of right answers is 0.50. A student taking a five-question true/false quiz gets 4 right out of 5. She says that this shows that she knows the material, because th

> What superpower do Americans want most? In past years, 10% of Americans chose invisibility as the most desired superpower, based on the Marist poll. Assume this is an accurate representation of all Americans. A group of futurists examines a more recent 2

> According to data released in 2016, 69% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 200 recent high school graduates is randomly selected. After verifying the conditions for the Central Li

> In 2018 it was estimated that approximately 45% of the American population watches the Super Bowl yearly. Suppose a sample of 120 Americans is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability t

> According to a 2018 Pew Research Center report on social media use, 28% of American adults use Instagram. Suppose a sample of 150 American adults is randomly selected. We are interested in finding the probability that the proportion of the sample who use

> According to a 2017 Pew Research Center report on voting issues, 59% of Americans feel that the everything should be done to make it easy for every citizen to vote. Suppose a random sample of 200 Americans is selected. We are interested in finding the pr

> Toss a fair six-sided die. The probability density function (pdf) in table form is given. Make a graph of the pdf for the die.

> According to the Brookings Institution, 50% of eligible 18- to 29-year-old voters voted in the 2016 election. Suppose we were interested in whether the proportion of voters in this age group who voted in the 2018 election was higher. Describe the two typ

> According to a 2017 Pew Research survey, 60% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the Internet. Suppose a random sample of 200 Americans from this age group is selected. a. What perce

> The average birth weight of domestic cats is about 3 ounces. Assume that the distribution of birth weights is Normal with a standard deviation of 0.4 ounce. a. Find the birth weight of cats at the 90th percentile. b. Find the birth weight of cats at the

> According to the National Health Center, the heights of 5-year-old boys are Normally distributed with a mean of 43 inches and a standard deviation of 1.5 inches. a. In which percentile is a 5-year-old boy who is 46.5 inches tall? b. If a 5-year-old boy w

> According to the National Health Center, the heights of 6-year-old girls are Normally distributed with a mean of 45 inches and a standard deviation of 2 inches. a. In which percentile is a 6-year-old girl who is 46.5 inches tall? b. If a 6-year-old girl

> College women have heights with the following distribution (inches): N (65, 2.5). a. Find the height at the 75th percentile. b. Find the height at the 25th percentile. c. Find the interquartile range for heights. d. Is the interquartile range larger or s

> A proponent of a new proposition on a ballot wants to know the population percentage of people who support the bill. Suppose a poll is taken, and 580 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test

> A proponent of a new proposition on a ballot wants to know whether the proposition is likely to pass. Suppose a poll is taken, and 580 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidenc

> For each question, find the area to the right of the given z-score in a standard Normal distribution. In this question, round your answers to the nearest 0.000.Include an appropriately labeled sketch of the N(0, 1) curve. a. z = 4.00 b. z = 10.00 (Hint:

> A magician has shaved an edge off one side of a six-sided die, and as a result, the die is no longer “fair.” The figure shows a graph of the probability density function (pdf). Show the pdf in table format by listing a

> Suppose a poll is taken that shows 220 out of 400 randomly selected Twitter users feel that Twitter should do more to decrease hateful and abusive content on the site. Test the hypothesis that the majority (more than 50%) of Twitter users feel the site s

> Some experts believe that 20% of all freshwater fish in the United States have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 250 fish tested, and 60 of them have dangerous levels of mercury. Test the hypothesis tha

> Historically (from about 2001 to 2014), 57% of Americans believed that global warming is caused by human activities. A March 2017 Gallup poll of a random sample of 1018 Americans found that 692 believed that global warming is caused by human activities.

> A 2018 Gallup poll of 2228 randomly selected U.S. adults found that 39% planned to watch at least a “fair amount” of the 2018 Winter Olympics. In 2014, 46% of U.S. adults reported planning to watch at least a “fair amount.” a. Does this sample give evide

> A 2018 Gallup poll of 3635 randomly selected Facebook users found that 2472 get most of their news about world events on Facebook. Research done in 2013 found that only 47% of all Facebook users reported getting their news about world events on Facebook.

> In a Northeastern University/ Gallup poll of 461 young Americans aged 18 to 35, 152 reported they would be comfortable riding in a self-driving car. Suppose we are testing the hypothesis that more than 30% of Americans in this age group would be comforta

> About 30% of the population in Silicon Valley, a region in California, are between the ages of 40 and 65, according to the U.S. Census. However, only 2% of the 2100 employees at a laid-off man’s former Silicon Valley company are between the ages of 40 an

> Samuel Morse determined that the percentage of a’s in the English language in the 1800s was 8%. A random sample of 600 letters from a current newspaper contained 60 a’s. Using the 0.10 level of significance, test the hypothesis that the proportion of a’s

> Samuel Morse determined that the percentage of t’s in the English language in the 1800s was 9%. A random sample of 600 letters from a current newspaper contained 48 t’s. Using the 0.10 level of significance, test the hypothesis that the proportion of t’s

> Suppose it is known that 60% of employees at a company use a Flexible Spending Account (FSA) benefit. a. If a random sample of 200 employees is selected, do we expect that exactly 60% of the sample uses an FSA? Why or why not? b. Find the standard error

> Determine whether each of the following variables would best be modeled as continuous or discrete. a. The weight of a car in pounds b. The weight of a car in kilograms

> Suppose it is known that 20% of students at a certain college participate in a textbook recycling program each semester. a. If a random sample of 50 students is selected, do we expect that exactly 20% of the sample participates in the textbook recycling

> According to one source, 50% of plane crashes are due at least in part to pilot error (http://www.planecrashinfo .com). Suppose that in a random sample of 100 separate airplane accidents, 62 of them were due to pilot error (at least in part.) a. Test the

> According to a 2017 Pew Research report, 40% of millennials have a BA degree. Suppose we take a random sample of 500 millennials and find the proportion who have a BA degree. a. What value should we expect for our sample proportion? b. What is the standa

> According to the 2017 SAT Suite of Assessments Annual Report, the average ERW (English, Reading, Writing) SAT score in Florida was 520. Assume the scores are Normally distributed with a standard deviation of 100. Answer the following including an appropr

> According to the 2017 SAT Suite of Assessments Annual Report, the average SAT math score for students in Illinois was 556. Assume the scores are Normally distributed with a standard deviation of 100. Answer the following including an appropriately labele

> The distribution of red blood cell counts is different for men and women. For both, the distribution is approximately Normal. For men, the middle 95% range from 4.5 to 5.7 million cells per microliter and for women, the middle 95% have red blood cells co

> The distribution of white blood cell count per cubic millimeter of whole blood is approximately Normal with mean 7500 and standard deviation 1750 for healthy patients. Use technology or a table to answer these questions. For each include an appropriately

> According to National Vital Statistics, the average length of a newborn baby is 19.5 inches with a standard deviation of 0.9 inches. The distribution of lengths is approximately Normal. Use technology or a table to answer these questions. For each includ

> Determine whether each of the following variables should best be modeled as continuous or discrete. a. The height of a person in inches b. The weight of a person in pounds

> Determine whether each of the following variables would best be modeled as continuous or discrete. a. The number of cars passing through an intersection in one hour b. The weight of a person

> Determine whether each of the following variables would best be modeled as continuous or discrete. a. The height of a high-rise apartment building b. The number of floors in a high-rise apartment building

> Sir William Blackstone (1723–1780) wrote influential books on common law. He made this statement: “All presumptive evidence of felony should be admitted cautiously; for the law holds it better that ten guilty persons escape, than that one innocent party

> According to a 2017 survey conducted by Netflix, 46% of couples have admitted to “cheating” on their significant other by streaming a TV show ahead of their partner. Suppose a random sample of 80 Netflix subscribers is selected. a. What percentage of the

> A test is conducted in which a coin is flipped 30 times to test whether the coin is unbiased. The null hypothesis is that the coin is fair. The alternative is that the coin is not fair. One of the accompanying figures represents the p-value after getting

> A researcher carried out a hypothesis test using a two-sided alternative hypothesis. Which of the following z-scores is associated with the smallest p-value? Explain. z = 0.50 z = 1.00 z = 2.00 z = 3.00

> According to the British Medical Journal, the distribution of weights of newborn babies is approximately Normal, with a mean of 3390 grams and a standard deviation of 550 grams. Use a technology or a table to answer these questions. For each include an a

> The length of gestation for hippopotami is approximately Normal, with a mean of 270 days and a standard deviation of 7 days. a. What percentage of hippos have a gestation period less than 260 days? b. Complete this sentence: Only 6% of hippos will have a

> Assume a standard Normal distribution. Draw a separate, well-labeled Normal curve for each part. a. Find an approximate z-score that gives a left area of 0.7000. b. Find an approximate z-score that gives a left area of 0.9500.

> Assume a standard Normal distribution. Draw a separate, well-labeled Normal curve for each part. a. Find the z-score that gives a left area of 0.7123. b. Find the z-score that gives a left area of 0.1587.

> In a standard Normal distribution, if the area to the left of a z-score is about 0.1000, what is the approximate z-score?

> In a standard Normal distribution, if the area to the left of a z-score is about 0.6666, what is the approximate z-score? First locate, inside the table, the number closest to 0.6666. Then find the z-score by adding 0.4 and 0.03; refer to the table. Draw

> The Normal model N(150, 10) describes the distribution of scores on the LSAT, a standardized test required by most law schools. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and th

> The Normal model N(69, 3) describes the distribution of male heights in the United States. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and then answer the given question. a. To b

> The average winter daily temperature in Chicago has a distribution that is approximately Normal, with a mean of 28 degrees and a standard deviation of 8 degrees. What percentage of winter days in Chicago have a daily temperature of 35 degrees or warmer?

> New York City’s mean minimum daily temperature in February is 27°F (http://www.ny.com). Suppose the standard deviation of the minimum temperature is 6°F and the distribution of minimum temperatures in February is approximately Normal. What percentage of

> According to Anthropometric Survey data, the distribution of arm spans for females is approximately Normal with a mean of 65.4 inches and a standard deviation of 3.2 inches. a. What percentage of women have arm spans less than 61 inches? b. Olympic swimm

> According to a 2017 AAA survey, 35% of Americans planned to take a family vacation (a vacation more than 50 miles from home involving two or more immediate family members. Suppose a recent survey of 300 Americans found that 115 planned on taking a family

> Bob Ross hosted a weekly television show, The Joy of Painting, on PBS in which he taught viewers how to paint. During each episode, he produced a complete painting while teaching viewers how they could produce a similar painting. Ross completed 30,000 pa

> According to Anthropometric Survey data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a standard deviation of 3.3 inches. a. What percentage of men have arm spans between 66 and 76 inches? b. Professional

> Assuming that the true proportion of success for the trials shown in the graph for Exercise 7.33 is 0.2, explain whether any of the graphs shows bias. Graph from exercise 7.33:

> Which of the dotplots given in Exercise 7.33 has the largest standard error, and which has the Smallest standard error? Exercise 7.33:

> In the graphs for Exercise 7.33, explain how you can tell from the shape of the graph which has the largest sample size and which has the smallest sample size. Graph from exercise 7.33:

> A Zener deck of cards has cards that show one of five different shapes with equal representation, so that the probability of selecting any particular shape is 0.20. A card is selected randomly, and a person is asked to guess which card has been chosen. T

> Suppose that, when taking a random sample of three students’ GPAs, you get a sample mean of 3.90. This sample mean is far higher than the collegewide (population) mean. Does that prove that your sample is biased? Explain. What else could have caused this

> According to The Washington Post, 72% of high school seniors have a driver’s license. Suppose we take a random sample of 100 high school seniors and find the proportion who have a driver’s license. a. What value should we expect for our sample proportion

> Suppose a shoe store stocks shoes in women’s sizes 5 through 9. These shoes will fit women with feet that are 21.6 through 25 centimeters long. What percentage of women will be able to find shoes that fit in this store? Use the statistics for the mean an