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statistics
elementary statistics in social research
Questions and Answers of
Elementary Statistics In Social Research
\(P_{97.5}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
\(P_{1.5}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
\(P_{25}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
\(P_{40}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
\(P_{91}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
\(P_{75}\)Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
Find the indicated z-score(s) shown in the graph. Area = 0.3520 Z z=? 0
Find the indicated z-score(s) shown in the graph. Area = 0.5987 0 z=?
Find the indicated z-score(s) shown in the graph. Area = 0.0233 0 z = ?
Find the indicated z-score(s) shown in the graph. z = ? 0 Area = 0.7190 Z
Find the indicated z-score(s) shown in the graph. Area = 0.05 Area = 0.05 z = ? 0 z = ? Z
Find the indicated z-score(s) shown in the graph. Area = 0.475 Area = 0.475 z = ? 0 z=? N
In a survey of 18-year old males, the mean weight was 166.7 pounds with a standard deviation of 49.3 pounds.(a) What weight represents the 95th percentile?(b) What weight represents the 43rd
Surveyors asked respondents to rate ten key aspects of their government’s response to the COVID-19 pandemic, including preparedness, communication, and material aid. A pandemic response score that
The length (in seconds) of the 100 most popular songs during the week of May 5, 2021, can be approximated by a normal distribution, as shown in the figure.(a) What song length represents the 5th
A water footprint is a measure of the appropriation of fresh water. The water footprint (in cubic meters) for a kilogram of wheat can be approximated by a normal distribution, as shown in the
The Advanced Dental Admission Test (ADAT) is designed so that the scores fit a normal distribution, as shown in the figure.(a) What is the minimum ADAT score that is in the top 5% of scores?(b)
The test scores for the analytical writing section of the Graduate Record Examination (GRE) can be approximated by a normal distribution, as shown in the figure.(a) What is the maximum score that can
The pregnancy durations (in days) for a population of new mothers can be approximated by a normal distribution, with a mean of 267 days and a standard deviation of 10 days.(a) What is the minimum
In a history class, the grades for various assessments are all positive numbers and have different distributions. Determine whether the grades for each assessment could be normally distributed.
\(P(x
\(P(x
\(P(160
\(P(172
In a survey of 19-year-old U.S. women, their heights were normally distributed, with a mean of 63.9 inches and a standard deviation of 3.3 inches. Find the probability that a randomly selected survey
In a survey of male infants from 3 to 5 months of age, head circumference was found to be normally distributed, with a mean of 42.9 centimeters and a standard deviation of 1.5 centimeters.Find the
The monthly utility bills in a city are normally distributed, with a mean of \($100\) and a standard deviation of \($12\). Find the probability that a randomly selected utility bill is (a) less than
Use the normal distribution in Exercise 13.(a) What percent of the SAT total scores are less than 1300?(b) Out of 1000 randomly selected SAT total scores, about how many would you expect to be
Use the normal distribution in Exercise 14.(a) What percent of the ACT composite scores are less than 19?(b) Out of 1500 randomly selected ACT composite scores, about how many would you expect to be
Use the normal distribution in Exercise 15.(a) What percent of the new mothers had a pregnancy length of less than 290 days?(b) What percent of the new mothers had a pregnancy length of between 260
Use the normal distribution in Exercise 16.(a) What percent of the adult males have a red blood cell count less than 6 million cells per microliter?(b) What percent of the adult males have a red
Given the mean of a normal distribution, how can you find the median?
Describe the inflection points on the graph of a normal distribution. At what x-values are the inflection points located?
Give two real-life examples of a continuous variable. Include one that is likely to be normally distributed. Explain your reasoning.
Explain how to transform a given x-value of a normally distributed variable x into a z-score.
In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. -0.9 0 z
To the left of z = -1.675.Find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the right of z = 2.215.Find the indicated area under the standard normal curve. If convenient, use technology to find the area.
The test scores for the Stanford-Binet Intelligence Scale are normally distributed with a mean score of 100 and a standard deviation of 16.The test scores of four students selected at random are 98,
The test scores for students who took the SAT (without the essay) are normally distributed with a mean score of 1051 and a standard deviation of 211.The test scores of four students selected at
\(P(z
\(P(z
\(P(-0.89
\(P(0
\(P(-1.78
\(P(-1.54
Which counting rule is used in the binomial probability formula?
A survey found that 29% of gamers own a virtual reality (VR) device. Ten gamers are randomly selected. The random variable represents the number who own a VR device.In Exercises 15–18, determine
Argentine soccer player Lionel Messi converts 78% of his penalty kicks. Suppose Messi takes six penalty kicks next season. Find the probability that the number he converts is(a) exactly six,(b) at
Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 16 consumers. Find the probability that the number of of consumers who
Five percent of the U.S. workforce test positive for illicit drugs. You randomly select 14 workers. Find the probability that the number who test positive for illicit drugs is(a) exactly two,(b) more
Sixty-six percent of people pronounce pecan “puh-CON” instead of “PEA-can.” You randomly select 15 people. Find the probability that the number of people who pronounce pecan “puh-CON”
Pennsylvania State University accepts 49% of applicants. You randomly select seven Pennsylvania State University applicants. The random variable represents the number who are accepted.In Exercises
Thirty-three percent of immigrants to the United States ages 25 and older have a bachelor’s degree or higher. You randomly select eight immigrants to the U.S. ages 25 and older. The random variable
Seventy-seven percent of adults want to live to age 100.You randomly select five adults and ask them whether they want to live to age 100.The random variable represents the number who want to live to
Eighty-five percent of U.S. adults believe cloning humans is morally wrong. You randomly select 10 U.S. adults and ask them whether they believe cloning humans is morally wrong. The random variable
Thirty-one percent of U.S. employees who are late for work blame oversleeping. You randomly select 12 U.S. employees who are late for work and ask them whether they blame oversleeping. The random
The probability of winning a game of rock-paper-scissors is 1/3.You play nine games of rock-paper-scissors. Find the probability that the number of games you win is (a) exactly five, (b) more than
Fifty-three percent of U.S. adults are currently married. You randomly select twelve U.S. adults. Find the probability that the number who are married is (a) exactly nine, (b) less than four, and (c)
Sixty percent of U.S. adults favor establishing policies to reduce the use of fossil fuels. You randomly select eight U.S. adults. Find the probability that the number who favor establishing policies
Eighteen percent of U.S. adults say they use Reddit. You randomly select seven U.S. adults. Find the probability that the number who use Reddit is (a) exactly one, (b) more than three, and (c) from
Let x represent the grade on an exam worth a total of 100 points.In Exercises 1 and 2, determine whether the random variable x is discrete or continuous. Explain.
Forty-two percent of U.S. adults have a gun in their home. You randomly select 12 U.S. adults. Find the probability that the number who have a gun in their home is(a) exactly two,(b) at least two,
Seventy-two percent of U.S. civilian employees have access to medical care benefits. You randomly select nine civilian employees. Find the probability that the number who have access to medical care
Sixty-two percent of candidates taking the Texas Bar Exam pass the test.You randomly select five Texas Bar Exam candidates. Find the probability that the number who pass is(a) exactly two,(b) at
Seventy-two percent of U.S adults have read a book in any format in the past year. You randomly select five U.S adults and ask them whether they have read a book in any format in the past year. The
Forty-nine percent of U.S adults answer correctly when asked “What is phishing?” You randomly select six U.S adults and ask them “What is phishing?” The random variable represents the number
Thirty-three percent of NCAA student-athletes have a job waiting for them when they graduate college. You randomly select ten NCAA student‑athletes who are graduating and ask them whether they have
Fourteen percent of noninstitutionalized U.S. adults smoke cigarettes.After randomly selecting ten noninstitutionalized U.S. adults, you ask them whether they smoke cigarettes. Find the probability
From 1940 to 2020, tornadoes killed about 0.26 people per day in the United States. Assume this rate holds true today and is constant throughout the year. Find the probability that the number of
In a recent season, hockey player Evgeni Malkin scored 25 goals in 55 games he played. Assume that his goal production stayed at that level for the next season. Find the probability that he would get
During a 10-year period, sharks killed an average of 6.4 people each year worldwide. Find the probability that the number of people killed by sharks next year is (a) exactly three, (b) more than six,
Sixty-nine percent of U.S. adults plan to get a COVID-19 vaccine or already have. You randomly select ten U.S. adults and ask them whether they plan to get a COVID-19 vaccine or already have. Find
Determine whether the random variable x is discrete or continuous. Explain your reasoning.(a) Let x represent the number of lightning strikes that occur in Wyoming during the month of June.(b) Let x
In the past year, thirty-three percent of U.S. adults have put off medical treatment because of the cost. You randomly select nine U.S. adults. Find the probability that the number who have put off
The five-year survival rate of people who undergo a liver transplant is 75%.The surgery is performed on six patients.(a) Construct a binomial distribution.(b) Graph the binomial distribution using a
Basketball player Stephen Curry makes a 3-pointer about 43% of the time.Find the probability that (a) the first 3-pointer he makes is the third shot,(b) the first 3-pointer he makes is the fourth or
One out of every 42 tax returns for incomes over $1 million requires an audit.An auditor is examining tax returns for over $1 million. Find the probability that (a) the first return requiring an
About 53% of U.S. full-time college students drank alcohol within a one-month period. You randomly select six U.S. full-time college students.Find the probability that the number who drank alcohol
The mean increase in the U.S. population is about 1.5 people per minute.Find the probability that the increase in the U.S. population in any given minute is (a) exactly three people, (b) more than
Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. (a) x 0 5 10 15 20 P(x) 0.03 0.09 0.19 0.32 (b) x 1 P(x) 20 1 23 4 10 -19 25
Fifty-six percent of federal student loans are in repayment. You randomly select five student loans and determine whether they are in repayment.The random variable represents the number that are in
The Centers for Disease Control and Prevention (CDC) is required by law to publish a report on assisted reproductive technology (ART). ART includes all fertility treatments in which both the egg and
The mean number of customers who arrive at the checkout counters each minute is 4.Create a Poisson distribution with \(\mu=4\) for \(x=0\) to 20 . Compare your results with the histogram shown at the
Minitab was used to generate 20 random numbers with a Poisson distribution for \(\mu=4\). Let the random number represent the number of arrivals at the checkout counter each minute for 20
Generate a list of 20 random numbers with a Poisson distribution for \(\mu=4\). Create a table that shows the number of customers waiting at the end of 1 through 20 minutes.In Exercises 1–7,
The mean increases to five arrivals per minute, but the store can still process only four per minute. Generate a list of 20 random numbers with a Poisson distribution for \(\mu=5\). Then create a
The mean number of arrivals per minute is five. What is the probability that 10 customers will arrive during the first minute?In Exercises 1–7, consider a grocery store that can process a total of
The mean number of arrivals per minute is four. Find the probability that(a) three, four, or five customers will arrive during the third minute.(b) more than four customers will arrive during the
The mean number of arrivals per minute is four. Find the probability that(a) no customers are waiting in line after one minute.(b) one customer is waiting in line after one minute.(c) one customer is
\({ }_{7} C_{5}={ }_{7} C_{2}\)In Exercises 3– 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?
A band is preparing a setlist of 21 songs for a concert. How many different ways can the band play the first six songs?
A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment.In how many different ways can the treatment group be selected?
The Saratoga Springs, New York, Zoning Board of Appeals has seven members. One member serves as board chair and another serves as vice chair. Given the names of the seven board members, what is the
The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23 board members, what is the probability of
A horse race has 10 entries. Given no information about the horses or jockeys, what is the probability of randomly selecting (in no particular order) the first three horses to finish the race?
You choose two music listeners at random. What is the probability that both say their primary source for new music is someone’s playlist?In Exercises 45 – 48, use the pie chart, which shows the
You choose three music listeners at random. What is the probability that all three say their primary source for new music is subscription music services?In Exercises 45 – 48, use the pie chart,
You choose nine music listeners at random. What is the probability that none of them say their primary source for new music is friends or social media?In Exercises 45 – 48, use the pie chart, which
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