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business statistics

Introductory Business Statistics 1st Edition Alexander Holmes , Barbara Illowsky , Susan Dean - Solutions

When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?Carbon-14 is a radioactive element with a half-life of about 5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.We are interested
Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks).a. Graph the probability distribution.b. f(x) = _________c. μ = _________d. σ = _________e. Find the probability that a person is
A random number generator picks a number from one to nine in a uniform manner.a. Graph the probability distribution.b. f(x) = _________c. μ = _________d. σ = _________e. P(3.5 < x < 7.25) = _________f. P(x > 5.67)g. P(x > 5 | x > 3) = _________ Carbon-14 is a radioactive element with a half-life
According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in
A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.a. Define the random variable. X = _______b. Graph the probability distribution.c. f(x) =
The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years.We randomly select one first grader from the class.a. Define the random variable. X = _________b. Graph the probability distribution.c. f(x) = _________d. μ = _________e. σ =
What is the average waiting time (in minutes)?a. zerob. twoc. threed. four The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.
The probability of waiting more than seven minutes given a person has waited more than four minutes is?a. 0.125b. 0.25c. 0.5d. 0.75 The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known
The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = 1/20 where x goes from 25 to 45 minutes.a. Define the random variable. X = ________b. Graph the probability distribution.c. The distribution is ______________ (name of distribution). It is
A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution.a. Find the average time between fireworks.b. Find probability that the time between fireworks is greater than four seconds.
The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.a. Find the probability that the truck driver goes more than 650 miles in a day.b. Find the probability that the truck drivers goes between 400 and 650 miles in a day.
Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.a. Define the random variable. X = ________________.b. Is X continuous or discrete?c. μ = ________d. σ = ________e. Draw
Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery.a. Define the random variable. X = _________________________________.b. Is X continuous or discrete?c. On average, how long would you expect one
The percent of persons (ages five and older) in each state who speak a language at home other than English is approximately exponentially distributed with a mean of 9.848. Suppose we randomly pick a state.a. Define the random variable. X = _________________________________.b. Is X continuous or
The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.a. Define the random variable. X =
The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of$150.a. Define the random variable. X = _________________________________.b. μ = ________c. σ = ________d. Draw a graph of the probability distribution. Label the axes.e. Find the
The decay rate is:a. 0.3333b. 0.5000c. 2d. 3
What is the probability that a phone will fail within two years of the date of purchase?a. 0.8647b. 0.4866c. 0.2212d. 0.9997
What is the median lifetime of these phones (in years)?a. 0.1941b. 1.3863c. 2.0794d. 5.5452
At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution.a. On average, how much time occurs between five consecutive calls?b. Find the probability that after a call is
In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential.a. What is the probability that an entire season
During the years 1998–2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.a. What is the probability that the next earthquake occurs within the next three months?b. Given that six
According to the American Red Cross, about one out of nine people in the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution.a. If 100 people arrive,
A web site experiences traffic during normal working hours at a rate of 12 visits per hour. Assume that the duration between visits has the exponential distribution.a. Find the probability that the duration between two successive visits to the web site is more than ten minutes.b. The top 25% of
At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.a. Find the probability that the time between two successive visits to the urgent care facility is less than 2 minutes.b. Find
Complete Table 4.1 using the data provided.A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.Let X = the number of years a new hire will stay with the company.Let
A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.Let X = the number of years a new hire will stay with the company.Let P(x) = the probability that a new hire will
A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.Let X = the number of years a new hire will stay with the company.Let P(x) = the probability that a new hire will
On average, how long would you expect a new hire to stay with the company?A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.Let X = the number of years a new hire
What does the column “P(x)” sum to?A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.Let X = the number of years a new hire will stay with the company.Let P(x) =
Define the random variable X.A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. X P(x) 1 0.15 2 0.35 3 0.40 4 0.10 Table 4.2
What is the probability the baker will sell more than one batch? P(x > 1) = _______ A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. X
What is the probability the baker will sell exactly one batch? P(x = 1) = _______ A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. X P(x)
On average, how many batches should the baker make?A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. X P(x) 1 0.15 2 0.35 3 0.40 4 0.10
Define the random variable X.A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution.Ellen has music practice three days a week. She practices for
Construct a probability distribution table for the data.A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution.Ellen has music practice three
We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8%
Define the random variable X.Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random.Javier volunteers in community events each month. He does not
What values does x take on?Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no
Construct a PDF table.Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5%
Find the probability that Javier volunteers for less than three events each month. P(x < 3) = _______ Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of
Find the probability that Javier volunteers for at least one event each month. P(x > 0) = _______ Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the
In words, define the random variable X.Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested
What values does X take on?Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the
In words, define the random variable X.Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested
X ~ _____(_____,_____)Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of
What values does the random variable X take on?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they believe that same-sex couples
Construct the probability distribution function (PDF).The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they believe that same-sex
On average (μ), how many would you expect to answer yes?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they believe that same-sex
What is the standard deviation (σ)?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they believe that same-sex couples should have
What is the probability that at most five of the freshmen reply “yes”?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they
What is the probability that at least two of the freshmen reply “yes”?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S.71.3% of those students replied that, yes, they
In words, define the random variable X.The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should
X ~ _____(_____,_____)The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to
What values does the random variable X take on?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples
Construct the probability distribution function (PDF). Stop at x = 6.The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe
On average (μ), how many freshmen would you expect to have to ask until you found one who replies "yes?"The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those
What is the probability that you will need to ask fewer than three freshmen?The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they
Assume the event occurs independently in any given day. Define the random variable X.On average, a clothing store gets 120 customers per day.
What values does X take on?On average, a clothing store gets 120 customers per day.
What is the probability of getting 150 customers in one day?On average, a clothing store gets 120 customers per day.
What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.On average, a clothing store gets 120 customers per day.
What is the probability that the store will have more than 12 customers in the first hour?On average, a clothing store gets 120 customers per day.
What is the probability that the store will have fewer than 12 customers in the first two hours?On average, a clothing store gets 120 customers per day.
Which type of distribution can the Poisson model be used to approximate? When would you do this?
Assume the event occurs independently in any given day. In words, define the random variable X.On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.
X ~ _____(_____,_____)On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.
What values does X take on?On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.
For the given values of the random variable X, fill in the corresponding probabilities.On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.
Is it likely that there will be no teens killed from motor vehicle injuries on any given day in the U.S? Justify your answer numerically.On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.
Is it likely that there will be more than 20 teens killed from motor vehicle injuries on any given day in the U.S.? Justify your answer numerically.On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving
A group of Martial Arts students is planning on participating in an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate
In one of its Spring catalogs, L.L. Bean® advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once.a. In words, define the random variable X.b. List the values
Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the
Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit. The nine are randomly chosen from eight volunteers from the Boston Celtics and four volunteers from the New England Patriots. We are interested in the number of Patriots picked.a. In words, define the random
A bridge hand is defined as 13 cards selected at random and without replacement from a deck of 52 cards. In a standard deck of cards, there are 13 cards from each suit: hearts, spades, clubs, and diamonds. What is the probability of being dealt a hand that does not contain a heart?a. What is the
According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery.Suppose that 1,000 babies from healthy baby
Define the random variable and list its possible values.Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to
State the distribution of X.Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are
Find the probability that at least four of the 25 patients actually have the flu.Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients
On average, for every 25 patients calling in, how many do you expect to have the flu?Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25
People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given Table 4.5. There is five-video limit per customer at this store, so nobody ever rents more than five DVDs.a. Describe the random variable X
A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.a.
The expected number of wins for that upcoming month is:a. 1.67b. 12c. 382/1043d. 4.43 Let X = the number of games won in that upcoming month.The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a
What is the probability that the San Jose Sharks win six games in that upcoming month?a. 0.1476b. 0.2336c. 0.7664d. 0.8903 The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a certain date). An
What is the probability that the San Jose Sharks win at least five games in that upcoming montha. 0.3694b. 0.5266c. 0.4734d. 0.2305
A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.
A student takes a 32-question multiple-choice exam, but did not study and randomly guesses each answer. Each question has three possible choices for the answer. Find the probability that the student guesses more than 75% of the questions correctly.
Six different colored dice are rolled. Of interest is the number of dice that show a one.a. In words, define the random variable X.b. List the values that X may take on.c. On average, how many dice would you expect to show a one?d. Find the probability that all six dice show a one.e. Is it more
More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses.a. In words, define the random variable X.b. List
Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.a. In words, define the random variable X.b. List the values that X may take on.c. Give the distribution of X. X ~ _____(_____,_____)d. How many are expected to attend their
At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the number of fencers who do not use the foil as their main weapon.a. In words, define the random variable X.b. List the values that X may take
Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number who participated in after-school sports all four years of high school.a. In words, define the random variable
The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20-year period. Assume each year is independent.a. In words, define the random variable X.b. List the values that X may
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.a. In words, define the random variable X.b. List the values that X may
There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and
According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X = the number of people who have access to electricity.a. What is the probability distribution for X?b. Using the formulas, calculate the mean
The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate in Afghanistan is 28.1%. Suppose you choose 15 people in Afghanistan at random. Let X = the number of people who are literate.a. Sketch a graph of the probability distribution
A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 28%. We are interested in the number of dealerships she must call.a. In words, define the
Suppose that the probability that an adult in America will watch the Super Bowl is 40%. Each person is considered independent. We are interested in the number of adults in America we must survey until we find one who will watch the Super Bowl.a. In words, define the random variable X.b. List the

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