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business statistics communicating

Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions

Scores on a management aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8.a. What is the probability that a randomly selected manager will score above 60?b. What is the probability that a randomly selected manager will score between 68 and 84? LO5
We can now answer the questions first posed by Akiko Hamaguchi in the introductory case of this chapter. Recall that Akiko is concerned about buying the right amount of salmon for daily consumption at Little Ginza. Akiko has estimated that the daily consumption of salmon is normally distributed
Let the time between e-mail messages during work hours be exponentially distributed with a mean of 25 minutes.a. Calculate the rate parameter λ .b. What is the probability that you do not get an e-mail for more than one hour?c. What is the probability that you get an e-mail within 10 minutes? LO5
Compute the mean and standard deviation of a lognormal random variable if the mean and the standard deviation of the underlying normal random variable are as follows: LO5a. μ = 0, σ = 1b. μ = 2, σ = 1c. μ = 2, σ = 1.5
The mileage (in thousands of miles) that car owners get with a certain kind of radial tire is a random variable Y having a lognormal distribution such that Y = ex where X is normally distributed. Let the mean and the standard deviation of the life of a radial tire be 40,000 miles and 5,000 miles,
The relief time provided by a standard dose of a popular children's allergy medicine averages six hours w ith a standard deviation of tw o hours.a. Determine the percentage of children who experience relief for less than four hours if the relief time follows a normal distribution.b. Determine the
According to the Federal Bureau of Investigation, there is a violent crime in the U.S. every 22 seconds (ABC News, September 25, 2007). Assume that the time between violent crimes is exponentially distributed.a. What is the probability that there is a violent crime in the U.S. in the next one
On a particularly busy section o f the Garden State Parkway in New Jersey, police use radar guns to detect speeders.Assume the tim e that elapses between successive speeders is exponentially distributed w ith a mean of 15 minutes.a. Calculate the rate parameter A.b. What is the probability of a
Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless Store. Lisa has been signing in an average of 48 new cell phone customers every month with a standard deviation of 22, while Brad signs in an average of 56 new customers with a standard deviation of 17. The store manager
On St. Patrick's Day, men spend an average of $43.87 while women spend an average of $29.54 (USA Today, March 17, 2009). Assume the standard deviations of spending for men and women are $3 and $11, respectively, and that both distributions are normally distributed.a. What is the probability that
U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger's, August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of
The revised guidelines from the National High Blood Pressure Education Program define normal blood pressure as readings below 120/80 millimeters of mercury (The New York Times, May 14, 2003). Prehypertension is suspected when the top number (systolic) is between 120 to 139 or when the bottom number
A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag is a uniformly distributed random variable that ranges from 10 to 12 pounds.a. Calculate the expected value and standard deviation of this distribution.b. Find the
A florist makes deliveries between 1:00 pm and 5:00 pm daily. Assume delivery times follow the continuous uniform distribution.a. Calculate the mean and variance of this distribution.b. Determine the percentage of deliveries that are made after 4:00 pm.c. Determine the percentage of deliveries that
It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a lognormal variable, Y = ex where X is normally distributed.Furthermore, let the mean and standard deviation of the life of a washing machine be 8 years
The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $39,626 and the median income is $33,600. A demographer decides to use
When crossing the Golden Gate Bridge, traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f(x) = 0.2e-2x\a. What is the mean waiting time that drivers
Customers make purchases at a convenience store, on average, every six minutes. It is fair to assume that the time between customer purchases is exponentially distributed.Jack operates the cash register at this store.a. What is the rate parameter A? What is the standard deviation of this
Let Y have the lognormal distribution with mean 82.8 and variance 156.25. Compute the following probabilities.a. P(Y > 100)b. P(80 < Y < 100) LO5
Let Y = ex, where X is normally distributed. Compute the mean and the variance of X given the following information.a. μ r = 14, σ2Y = 22b. μ r = 20, σ2Y=22 C. μ r = 20, σ2 Y =120 LO5
Compute the mean and the variance of a lognormal variable Y = ex where X is normally distributed with the following mean and variance: LO5a. μ = 3, σ 2 = 2b. μ = 5, σ 2 = 2c. μ = 5, σ 2 = 3
A random variable X is exponentially distributed with a probability density function of f(x) = 5e-5x. Calculate the mean and the standard deviation of X. LO5
A random variable X is exponentially distributed with an expected value of 25.a. What is the rate parameter λ ? What is the standard LO5 deviation o f X?b. Compute P(20 ≤ X ≤ 30).c. Compute P(15 ≤ X ≤ 35).
A random variable X is exponentially distributed w ith a mean o f 0.1.a. What is the rate parameter A? What is the standard deviation o f X?b. Compute P(X > 0.20).c. Compute P(0.10≤ X ≤ 0.20). LO5
You are considering the risk-return profile of tw o mutual funds for investment. The relatively risky fund promises an expected return of 8% w ith a standard deviation of 14%. The relatively less risky fund promises an expected return and standard deviation of 4% and 5%, respectively.Assume that
A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for$300,000, the company believes that it will be able to get an average sale
A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. What is the risk (standard deviation) that this investment manager has assumed in his calculation if it is known that returns are normally distributed with a mean of
Average talk time between charges of a cell phone is advertised as 4 hours. Assume that talk time is normally distributed with a standard deviation of 0.8 hour.a. Find the probability that talk time between charges for a randomly selected cell phone is below 3.5 hours.b. Find the probability that
Scores on a marketing exam are known to be normally distributed with mean and standard deviation of 60 and 20, respectively.a. Find the probability that a randomly selected student scores between 50 and 80.b. Find the probability that a randomly selected student scores between 20 and 40.c. The
An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (New York Times, April 17,2009). It is also known that the average cumulative debt of recent college graduates is about $22,500. Let the cumulative debt among recent college graduates be normally
The manager of a night club in Boston stated that 95% of the customers are between the ages of 22 and 28 years. If the age of customers is normally distributed w ith a mean of 25 years, calculate its standard deviation. LO5
Recent research suggests that Americans make an average of 10 phone calls per day (CNN, August 26, 2010). Let the number of calls be normally distributed with a standard deviation of 3 calls.a. What is the probability that an average American makes between 4 and 12 calls per day?b. What is the
The time required to assemble an electronic component is normally distributed with a mean and standard deviation of 16 minutes and 8 minutes, respectively.a. Find the probability that a randomly picked assembly takes between 10 and 20 minutes.b. It is unusual for the assembly time to be above 24
Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall Street Journal, August 26, 2010).Let the rate of seriously delinquent loans follow a normal
According to the Bureau of Labor Statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2 , 2008). Assume that the probability distributions are normal and that the standard deviation is 2
The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds.a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds.b. Find the probability that a randomly selected turkey weighs below 12 pounds. LO5
Americans are increasingly skimping on their sleep (National Geographic News, February 2 4 , 2005). A health expert believes that American adults sleep an average of 6.2 hours on weekdays with a standard deviation of 1.2 hours. To answer the following questions, assume that sleep time on weekdays
The average high-school teacher annual salary is$43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000.a. What percent of high school teachers make between$40,000 and $50,000?b. What percent of high school teachers make more
The random variable X is normally distributed. Also, it is known th a tP (X > 150) = 0.10.a. Find the population mean μ if the population standard deviation σ = 15.b. Find the population mean μ if the population standard deviation σ = 25.c. Find the population standard deviation σ if the
Let X be normally distributed with mean μ = 2500 and standard deviation σ = 800.a. Find x such that P(X ≤ x) = 0.9382.b. Find x such that P(X > x) = 0.025.c. Find x such that P(2500 ≤ X ≤ x) = 0.1217.d. Find x such that P(X ≤ x) = 0.4840. LO5
Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2.a. Find P(X > 7.6).b. Find P(7.4≤ X ≤ 10.6).c. Find x such that P(X > x) = 0.025.d. Find x such that P(x ≤ X≤ 2.5) = 0.4943. LO5
Let X be normally distributed with mean μ = 120 and standard deviation σ = 20.a. Find P(X≤ 86).b. Find P(80≤ X ≤ 100).c. Find x such that P(X ≤ x) = 0.40.d. Find x such that P(X > x) = 0.90. LO5
Let X be normally distributed with mean μ = 10 and standard deviation σ = 4. LO5a. Find P(X ≤ 0).b. Find P(X > 2).c. Find P(4 ≤ X ≤ 10).d. Find P(6 ≤ X ≤ 14).
Let X be normally distributed with mean μ = 10 and standard deviation σ = 6. LO5a. Find P(X ≤ 0).b. Find P[X > 2).c. Find P(4 ≤ X ≤ 10).d. Find P(6 ≤ X ≤ 14).
A professional basketball team averages 80 points per game with a standard deviation of 10 points. Assume points per game follow the normal distribution. Use the empirical rule to answer the following questions.a. What percentage of scores are between 60 and 100 points?b. What percentage of scores
The average rent in a city is $1,500 per m onth with a standard deviation of $250. Assume rent follows th e normal distribution.Use th e empirical rule to answ er th e following questions.a. W hat percentage of rents are betw een $1,250 and $1,750?b. W hat p ercen tag e of rents are less th an
Assum e th a t IQ scores follow a norm al distribution with a m ean of 100 and a standard deviation of 16. Use th e em pirical rule to answ er th e follow ing questions.a. W hat p ercen tag e of peo p le score betw een 84 and 116?b. W hat p ercen tag e of people score less th an 68? LO5
The historical returns on a balanced portfolio have had an average return of 8% and a standard deviation of 12%.Assume that returns on this portfolio follow a normal distribution. Use the empirical rule to answer the following questions.a. What percentage of returns were greater than 20%?b. What
Find the following z values for the standard normal variable Z. LO5a. P(Z≤ z) = 0.1020b. P(z≤ Z ≤ 0) = 0.1772c. P(Z >z) = 0.9929d. P(0.40≤ Z ≤ z) = 0.3368
Find the following z values for the standard normal variable Z. LO5a. P(Z ≤ z) = 0.9744b. P (Z > z ) = 0.8389c. P ( - z ≤ Z ≤ z) = 0.95d. P(0≤ Z ≤ z) = 0.3315
Find the following probabilities based on a standard normal variable Z. LO5a. P(-0 .6 7 ≤ Z ≤ -0.23)b. P(0 ≤ Z ≤ 1.96)c. P( - 1 .2 8 ≤ Z ≤ 0)d. P(Z > 4.2)
Find the following probabilities based on a standard normal variable Z. LO5a. P(Z > 0.74)b. P(Z ≤ -1.92)c. P(0 ≤ Z ≤ 1.62)d. P( - 0 .9 0 ≤ Z ≤ 2.94)
Find the following probabilities based on a standard normal variable Z. LO5a. P(Z > 1.32)b. P(Z ≤ -1.32)c. P(1 .3 2 < Z < 2 .3 7 )d. P( - 1 .3 2 ≤ Z ≤ 2.37)
The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:15 am and a late arrival time of 9:55 am.a. Calculate the mean and standard deviation of the
The Netherlands is one of the world leaders in the production and sale of flowers. Suppose the heights of the tulips in the greenhouse of Rotterdam's Fantastic Flora follow a continuous uniform distribution with a lower bound of 7 inches and an upper bound of 16 inches. You have come to the
The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4 minutes.a. Calculate the expected arrival time.b. What is the probability that an elevator arrives in less than 11/2 minutes?c. What is the probability that the wait for an elevator is more
Suppose the average price of electricity for a New England customer follows the continuous uniform distribution with a lower bound of 12 cents per kilowatt-hour and an upper bound of 20 cents per kilowatt-hour.a. Calculate the average price of electricity for a New England customer.b. What is the
A random variable X follows the uniform distribution with a lower lim it of 750 and an upper lim it of 800.a. Calculate the mean and standard deviation of this distribution.b. What is the probability that X is less than 770?Applications LO5
A random variable X follows the continuous uniform distribution with a lower lim it of 10 and an upper lim it of 30.a. Calculate the mean and standard deviation of the distribution.b. What is the probability that X is greater than 22?c. What is the probability that X is between 15 and 23? LO5
A random variable X follows the continuous uniform distribution with a lower bound of - 2 and an upper bound of 4.a. What is the height of the density function f(x)?b. What are the mean and the standard deviation of the distribution?c. Calculate P(X ≤ — 1). LO5
A random variable X follows the continuous uniform distribution with a lower bound of 5 and an upper bound of 35.a. What is the height of the density function f(x)lb. What is the mean and the standard deviation of the distribution?c. Calculate P(X > 10). LO5
For a continuous random variable X, P[20 ≤ X ≤ 40) = 0.15 and P(X > 4 0 ) = 0.16. Calculate the following probabilities. LO5a. P(X < 40)b. P(X < 20)c. P(X = 40)
For a continuous random variable X with an upper bound of 4, P(0 ≤ X ≤ 2.5) = 0.54 and P{2.5 ≤ X ≤ 4) = 0.16.Calculate the following probabilities. LO5a. P(X< 0)b. P(X > 2.5)c. P(0 ≤ X ≤ 4)
The cumulative probabilities for a continuous random variable X are P(X ≤ 10) = 0.42 and P(X ≤ 20) = 0.66.Calculate the following probabilities. LO5a. P(X > 10)b. P(X > 20)c. P(10 < X < 20)
Calculate and interpret probabilities for a random variable that follows the lognormal distribution. LO5
Calculate and interpret probabilities for a random variable that follows the exponential distribution. LO5
Calculate and interpret probabilities for a random variable that follows the normal distribution. LO5
Use the standard normal table or the z table. LO5
Explain the characteristics of the normal distribution. LO5
Describe a continuous uniform distribution and calculate associated probabilities. LO5
Describe a continuous random variable. LO5
Discuss point estimators and their desirable properties. P-69
Explain an interval estimator. P-69
Calculate a confidence interval for the population mean when the population standard deviation is known. P-69
Describe the factors that influence the width of a confidence interval. P-69
Discuss features of the t distribution. P-69
Calculate a confidence interval for the population mean when the population standard deviation is not known. P-69
Calculate a confidence interval for the population proportion. P-69
Select a sample size to estimate the population mean and the population proportion. P-69
A random sam ple produced th e follow ing data: P-69Calculate th e point estim ate of th e population m ean. 135 120 127 132 123 130
A random sam ple produced th e following data: P-69Calculate th e point e stim ate of th e population m ean. 0 -10 -8 2 6
A random sam ple of 50 observations results in 20 successes.a. Calculate th e point estim ate of th e population proportion of successes.b. Calculate th e point estim ate of th e population proportion of failures. P-69
A random sam ple of 400 observations results in 300 successes.a. Calculate th e point estim ate of th e population proportion of successes.b. Calculate th e point estim ate of th e population proportion of failures. P-69
A random sam ple of eig h t drugstores show s th e following prices (in $) of a popular pain reliever:Calculate th e point estim ate of th e population m ean price for th e pain reliever. P-69 2.99 3.25 2.75 3.05 3.10 2.95 2.99 3.25
As reported by tradingeconom ics.com in 2011, the unem ploym ent rates (in %) in m ajor econom ies around the world are as follows: P-69Calculate th e point estim ate of th e u nem ploym ent rate in m ajor econom ies around th e world. Country Unemployment Rate (in %) France 9.6 India 9.4 United
A recent survey asked 5,324 individuals: What's most important to you when choosing where to live? The responses are shown by the following frequency distribution. P-69a. Calculate the point estimate of the population proportion of those who believe that low crime is most important.b. Calculate the
A survey conducted by CBS News asked 1,026 respondents: "What would you do with an unexpected tax refund?" The responses are summarized in the following table. P-69a. Calculate the point estimate of the population proportion of those who would put the tax refund in the bank.b. Calculate the point
Find zα /2 for each of the following confidence levels used in estimating the population mean. P-69a. 90%b. 98%c. 88%
Find zα /2 for each of the following confidence levels used in estimating the population mean. P-69a. 89%b. 92%c. 96%
Consider a population with a known standard deviation of 26.8. In order to compute an interval estimate of the population mean, a sample of 64 observations is drawn,a. Is the condition that is normally distributed satisfied?b. Compute the margin of error at a 95% confidence level.c. Compute the
Discuss the factors that influence the margin of error of the confidence interval of the population mean.What can a practitioner do to reduce the margin of error? P-69
The average life expectancy for Bostonians is 78.1 years(The Boston Globe, August 1 6 , 2010). Assume that this average was based on a sample of 50 Bostonians and that the population standard deviation is 4.5 years.a. What is the point estimate of the population mean?b. At 90% confidence, what is
A family is relocating from St. Louis, Missouri, to California.Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help
U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger's, August 2007). Assume that this average was based on a sample of 100 consumers and that the population standard deviation is
Find tα,df from the following information. P-69a. α = 0.025 and d f = 12b. α = 0 .1 0 and d f = 12c. α = 0.025 and d f = 25d. α = 0.10 and d f = 25
A random sample of 24 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 104.6 and 28.8, respectively.Assume that the population is normally distributed.a. Construct a 90% confidence interval of the population mean.b. Construct
Consider a normal population with an unknown population standard deviation. A random sample results in and s2 = 33.64.a. Compute a 95% confidence interval for μ if and s2 were obtained from a sample of 16 observations,b. Compute a 95% confidence interval for μ if and s2 were obtained from a
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 2 2 , 1 8 , 1 4 , 2 5 , 1 7 , 2 8 , 1 5 , 20.a. Calculate the sample mean and the sample standard deviation.b. Construct the 80% confidence interval of the population mean.c.
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 1 2 0 , 130, 9 0 , 2 0 5 , 185, and 220. She believes that the number of customers served on weekdays follows a normal distribution. Construct a 90% confidence interval
The Sudoku puzzle has recently becom e very popular all over the world. It is based on a 9 × 9 grid and the challenge is to fill in the grid so that every row, every column, and every 3 × 3 box contains the digits 1 through 9. A researcher is interested in estimating the average time taken by a

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