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Statistics
In 1898, Ladislaus von Bortkiewicz published The Law of Small Numbers, in which he demonstrated the power of the Poisson probability law. Before his publication, the law was used exclusively to
The number of hits to a website follows a Poisson process and occurs at the rate of 10 hits per minute between 7:00 p.m. and 9:00 p.m. How long should you expect to wait before the probability of at
Assuming μ = 5, compute(a) P(6)(b) P(X < 6)(c) P(X ≥ 62(d) P(2 ≤ X ≤ 4)The random variable X follows a Poisson process with the given mean.
Assuming μ = 7, compute(a) P(10)(b) P(X < 10)(c) P(X ≥ 10)(d) P(7 ≤ X ≤ 9)The random variable X follows a Poisson process with the given mean.
Assuming λ = 0.07 and t = 10, compute(a) P(4)(b) P(X < 4)(c) P(X ≥ 4)(d) P(4 ≤ X ≤ 6)(e) μX and σXThe random variable X follows a Poisson process with the given value of λ and t.
State the conditions required for a Poisson process.
The random variable X follows a Poisson process with l = 0.05 and t = 30. Find each of the following: (a) P(2) (b) P(X < 2) (c) P(X ≥ 2) (d) P(1 ≤ X ≤ 3) (e) What are μX and σX?
The mills at the Acme Carpet Company produce, on average, one flaw in every 500 yards of material produced; the carpeting is sold in 100-yard rolls. If the number of flaws in a roll follows a Poisson
The student copy machine in the library requires a maintenance call an average of two times per month. Assuming that the number of required maintenance calls follows a Poisson distribution, would it
The Stanley Cup is a best-of-seven series to determine the champion of the National Hockey League. The following data represent the number of games played, X, in the Stanley Cup before a champion was
1. Using the information provided, describe, through graphical summaries and numerical summaries such as the mean and standard deviation, each probability distribution.2. Does it appear that, on
1. A _______ ______ ______ is an equation used to compute probabilities of continuous random variables.2. A ______ is an equation, table, or graph used to describe reality.3. True or False: The
(a) Find the probability that your friend is between 5 and 10 minutes late.(b) It is 10 a.m. There is a 40% probability your friend will arrive within the next minutes.
(a)Find the probability that your friend is between 15 and 25 minutes late.(b)It is 10 a.m. There is a 90% probability your friend will arrive within the next minutes.
Find the probability that your friend is at least 20 minutes late.
Find the probability that your friend is no more than 5minutes late.
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution.(a) Draw the graph of
The graph of a normal curve is given. Use the graph to identify the values of m and s.1.2.3.4.
Draw a normal curve and label the mean and inflection points.1. μ = 30 and σ = 102. μ = 50 and σ = 5
The following data represent the heights (in inches) of 80 randomly selected five year- old females.(a) Use statistical software to construct a relative frequency histogram. Comment on the shape of
Researchers conducted a prospective cohort study in which male patients who had an out-of-hospital cardiac arrest were submitted to therapeutic hypothermia (intravenous infusion of cold saline
Determine whether the graph can represent a normal curve. If it cannot, explain why.1.2. 3. 4. 5. 6.
Find the z-score such that the area under the standard normal curve to its left is 0.1.Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution.
Find the z-score such that the area under the standard normal curve to its left is 0.2. Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution.
Find the z-score such that the area under the standard normal curve to its right is 0.25.Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution.
Find the z-score such that the area under the standard normal curve to its right is 0.35.Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution.
Find z-scores that separate the middle 99% of the distribution from the area in the tails of the standard normal distribution.Find the indicated z-score. Be sure to draw a standard normal curve that
Find the z-scores that separate the middle 94% of the distribution from the area in the tails of the standard normal distribution.Find the indicated z-score. Be sure to draw a standard normal curve
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) Draw a normal model that describes the
In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after
Explain why P(X ˃ 30) should be reported as <0.0001 if X is a normal random variable with mean 100 and standard deviation 15.
Explain why P(X ≤ 2202 should be reported as ˃0.9999 if X is a normal random variable with mean 100 and standard deviation 15.
The data represent the time spent waiting in line (in minutes) for the Demon Roller Coaster for 100 randomly selected riders. Retrieve the data 7_3_13 at www.pearsonhighered.com/sullivanstats using
use the results in the table to (a) draw a normal probability plot, (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table
A random sample of 20 undergraduate students receiving student loans was obtained, and the amount of their loans for the 2014-2015 school year was recorded.use a normal probability plot to assess
1. In a binomial experiment with n trials and probability of success p, if_____ , the binomialrandom variable X is approximately normal with μX _____= and σX =__________ .2. When adding or
Use the results in the table to(a) draw a normal plot,(b) determine the linear correlation between the observed values and expected z-scores,(c) determine the critical value in Table VI to assess the
Hector obtained a random sample of twenty recent college graduates who own cars and asked each to disclose the age of their car (in months). Is it reasonable to conclude that age of car is normally
Explain how to use a normal probability plot to assess normality.
Abby Tudor recently turned 40. Her knees ache and she feels shortness of breath during exercise, along with periodic dizziness and general fatigue. Despite trying various diet and exercise regimes,
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
1. True or False: The distribution of the sample mean, x, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.2. True
Suppose you want to study the number of hours of sleep full-time college students at your college get each evening. To do so, you obtain a list of full-time students at your college, obtain a simple
A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a
According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47.(a) Suppose a random sample of 200 Americans is asked to disclose
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82.(a) Suppose a random sample of 100 Americans
The Pew Research Center recently reported that 18% of women 40-44 years of age have never given birth. Suppose a random sample of 250 adult women 40-44 years of age results in 52 indicating they have
A researcher studying ADHD among teenagers obtains a simple random sample of 100 teenagers aged 13-17 and asks them whether or not they have ever been prescribed medication for ADHD. To say that the
Suppose 21% of all American teens (age 13-17 years) believe in reincarnation.(a) Bob and Alicia both obtain a random sample of 100 American teens and ask each participant to disclose
Consider the homeowners association presented at the beginning of this section. A random sample of 20 households resulted in 15 indicating that they would favor an increase in assessments. Explain
In Chapter 6, we learned that the proportion of passengers who miss a flight for which they have a reservation is 0.0995.(a) Suppose a flight has 290 reservations. What is the
In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a finite population in which n ˃ 0.05N, the standard
The New England Patriots made headlines prior to the 2015 Super Bowl for allegedly playing with underinflated footballs. An underinflated ball is easier to grip, and therefore, less likely to be
1. True or False: The population proportion and sample proportion always have the same value. 2. True or False: The mean of the sampling distribution of p̂ is p.
What happens to the standard deviation of p̂ as the sample size increases? If the sample size is increased by a factor of 4, what happens to the standard deviation of p̂?
In the questions below, describe the sampling distribution of p̂. Assume that the size of the population is 25,000 for each problem.1. n = 500, p = 0.42. n = 300, p = 0.7
What are the mean and standard deviation of the sampling distribution of x̅ ? What are the mean and standard deviation of the sampling distribution of p̂?
The total energy need during pregnancy is normally distributed, with mean µ = 2600 kcal/day and standard deviation σ = 50 kcal/day. Source: American Dietetic Association(a) Is total energy need
A Gallup survey indicated that 72% of 18- to 29-year-olds, if given a choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18- to 29-year-olds is
According to the U.S. Census Bureau, in 2009, 10% of adults 25 years and older in the United States had advanced degrees. A researcher with the U.S. Department of Education surveys 500 randomly
The exponential distribution is an example of a skewed distribution. It is defined by the density functionwith parameter l. The mean of an exponential distributionThe exponential distribution is used
Fill in the blanks.1. A __________ is the value of a statistic that estimates the value of a parameter.2. The _______________ represents the expected proportion of intervals that will contain the
In following question determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the sample with the specified
A Rasmussen Reports national survey of l000 adult Americans found that 18% dreaded Valentine's Day. The margin of error for the survey was 4.5 percentage points with 95% confidence? Explain what this
A Gallup poll of 547 adult Americans employed full or part time asked, "Generally speaking, would you say your commute to work is-very stressful, somewhat stressful, not that stressful, or not
A survey of 2306 adult Americans aged 18 and older conducted by Harris Interactive found that 417 have donated blood in the past two years. (a) Obtain a point estimate for the population proportion
Low levels of testosterone in adult males may be treated using AndroGel 1.62%. In clinical studies of 234 adult males who were being treated with AndroGel 1.62%, it was found that 26 saw their
In a survey of 700 community college students, 481 indicated that they have read a book for personal enjoyment during the school year (based on data from the Community College Survey of Student
In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included
Go to www.pearsonhighered.com/sullivanstats to obtain the data file 9_1_33 using the file format of your choice for the version of the text you are using. The data represent the daily (for example,
Explain what "95% confidence" means in a 95% confidence interval?
Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently
In following question determine the critical value za/2 that corresponds to the given level of confidence.1. 90%2. 99%3. 98%4. 92%
1. As the number of degrees of freedom in the t-distribution increases, the spread of the distribution ____________ (increases/decreases). 2. True or False: The t-distribution is centered at (. 3.
A random sample of 51 fatal crashes in 2013 in which the driver had a positive blood alcohol concentration (BAC) from the National Highway Traffic Safety Administration results in a mean BAC of 0.167
How much time do Americans spend eating or drinking? Suppose for a random sample of 1001 Americans age 15 or older, the mean amount of time spent eating or drinking per day is 1.22 hours with a
A Tootsie Pop is a sucker with a candy center. A famous commercial for Tootsie Pops once asked, "How many licks to the center of a Tootsie Pop?" In an attempt to answer this question, Cory Heid of
The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal probability plot suggests the data could come from a population that is
The following data represent the repair cost for a low-impact collision in a simple random sample of mini- and micro-vehicles (such as the Chevrolet Aveo or Mini Cooper).(a) Draw a normal probability
The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers conducted by Essential Baby.(a) Draw a normal probability plot to determine if it is
The following data represent the number of housing starts predicted for the 2nd quarter (April through June) of 2014 for a random sample of 40 economists.(a) Draw a histogram of the data. Comment on
The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 6.16 represents 6,160,000 shares traded), represent the volume of PepsiCo stock
Go to www.pearsonhighered.com/sullivanstats to obtain the data file 9_2_37 using the file format of your choice for the version of the text you are using. The data represent the width (in yards) and
The Sullivan Statistics Survey II asks, "What percent of one's income should an individual pay in federal income taxes?" Go to www.pearsonhighered.com/sullivanstats to obtain the data file
The General Social Survey asked respondents, "If ever married, how old were you when you first married?" The results are summarized in the Minitab output that follows:One-Sample T: AGEWEDVariable
A question on the General Social Survey was, "When you drink, how many drinks do you have?" The survey was administered to a random sample of 243 adult Americans aged 21 or older. Go to
Suppose you have two populations: Population A-All students at Illinois State University (N = 21,000) and Population B-All residents of the city of Homer Glen, IL (N = 21,000). You want to estimate
In following question a simple random sample of size n 6 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected
1. True or False: The chi-square distribution is symmetric. 2. True or False: The shape of the chi-square distribution depends on its degrees of freedom. 3. True or False: To construct a confidence
The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal probability plot suggests the data could come from a population that is
Travelers pay taxes for flying, car rentals, and hotels. The following data represent the total travel tax for a 3-day business trip in eight randomly selected cities. Note: Chicago has the highest
The following data represent the repair cost for a low-impact collision in a simple random sample of mini and micro-vehicles (such as the Chevrolet Aveo or Mini Cooper). In Problem 33 from Section
A jar of peanuts is supposed to have 16 ounces of peanuts. The filling machine inevitably experiences fluctuations in filling, so a quality-control manager randomly samples 12 jars of peanuts from
Investors not only desire a high return on their money, but they would also like the rate of return to be stable from year to year. An investment manager invests with the goal of reducing volatility
Sir R. A. Fisher, a famous statistician, showed that the critical values of a chi-square distribution can be approximated by the standard normal distributionwhere v is the degrees of freedom and zk
In following question find the critical values x21- α/2 and x2α/2 for the given level of confidence and sample size. 1. 90% confidence, n = 20 2. 95% confidence, n = 25 3. 98% confidence, n = 23 4.
Clayton Kershaw of the Los Angeles Dodgers is one of the premier pitchers in baseball. His most popular pitch is a four-seam fastball. The data in the next column represent the pitch speed (in miles
In March 2014, Harris Interactive conducted a poll of a random sample of 2234 adult Americans 18 years of age or older and asked, "Which is more annoying to you, tailgaters or slow drivers who stay
Sleep apnea is a disorder in which you have one or more pauses in breathing or shallow breaths while you sleep. In a cross-sectional study of 320 individuals who suffer from sleep apnea, it was found
Estimate the standard deviation of a Clayton Kershaw fastball with 95% confidence. See Problem 19.Refer to Problem 19, Clayton Kershaw of the Los Angeles Dodgers is one of the premier pitchers in
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