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Business Statistics
Find the average age of the cars in the lot.
Find the probability that a randomly chosen car in the lot was less than four years old.a. Sketch the graph, and shade the area of interest.b. Find the probability. P(x
Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old.a. Sketch the graph, shade the area of interest.b. Find the
What has changed in the previous two problems that made the solutions different?The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to
Find the third quartile of ages of cars in the lot. This means you will have to find the value such that 3/4, or 75%, of the cars are at most (less than or equal to) that age.a. Sketch the graph, and
What type of distribution is this?A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer
Are outcomes equally likely in this distribution? Why or why not?A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of
What is m? What does it represent?A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer
What is the mean?A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by
What is the standard deviation?A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can
State the probability density function.A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each
Graph the distribution.A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be
Find P(2 < x < 10).A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by
Find P(x > 6).A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the
Find the 70th percentile.A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be
What is m?A distribution is given as X ~ Exp(0.75).
What is the probability density function?A distribution is given as X ~ Exp(0.75).
Draw the distribution.A distribution is given as X ~ Exp(0.75).
Find P(x < 4).A distribution is given as X ~ Exp(0.75).
Find the 30th percentile.A distribution is given as X ~ Exp(0.75).
Find the median.A distribution is given as X ~ Exp(0.75).
Which is larger, the mean or the median?
What is being measured here?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
Are the data discrete or continuous?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
In words, define the random variable X.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
What is the decay rate (m)?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
The distribution for X is ______.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
Find the amount (percent of one gram) of carbon-14 lasting less than 5,730 years. This means, find P(x a. Sketch the graph, and shade the area of interest.b. Find the probability. P(x We are
Find the percentage of carbon-14 lasting longer than 10,000 years.a. Sketch the graph, and shade the area of interest.b. Find the probability. P(x > 10,000) = ________ Carbon-14 is a radioactive
Thirty percent (30%) of carbon-14 will decay within how many years?a. Sketch the graph, and shade the area of interest.b. Find the value k such that P(x Carbon-14 is a radioactive element with a
Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if
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
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
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) =
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
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
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
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
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
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
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 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
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
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 =
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
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
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 =
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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