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Questions and Answers of Statistics

A committee of 40 members consists of 24 men and 16 women. A subcommittee consisting of ten randomly selected members will be formed.a. What are the expected number of men and women in the
Powerball is a jackpot game with a grand prize starting at $20 million and often rolling over into the hundreds of millions. In 2006, the jackpot was $365 million.The winner may choose to receive the
A professor uses a relative scale for grading. She announces that 60% of the students will get at least a B, with 15% getting A’s. Also, 5% will get a D and another 5% will get an F. Assume that no
Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none.a. Find the expected value and
Rent-to-own (RTO) stores allow consumers immediate access to merchandise in exchange for a series of weekly or monthly payments. The agreement is for a fixed time period. At the same time, the
Forty-four percent of consumers with credit cards carry balances from month to month (bankrate.com, February 20, 2007).Four consumers with credit cards are randomly selected.a. What is the
Apple products have become a household name in America with 51% of all households owning at least one Apple product (CNN, March 19, 2012).a. What is the probability that two in a random sample of
Twenty percent of U.S. mortgages are “underwater” (The Boston Globe, March 5, 2009). A mortgage is considered underwater if the value of the home is less than what is owed on the mortgage.
According to a survey by consulting firm Watson Wyatt, approximately 19% of employers have eliminated perks or plan to do so in the next year (Kiplinger’s Personal Finance , February 2009). Suppose
Studies have shown that bats can consume an average of ten mosquitoes per minute (berkshiremuseum.org).a. Calculate the average number of mosquitoes that a bat consumes in a 30-second interval.b.
The police have estimated that there are twelve major accidents per day on a particular 10-mile stretch of a national highway.Suppose the incidence of accidents is evenly distributed in this 10-mile
Suppose you draw three cards, without replacement, from a deck of well shuffled cards. Remember that each deck consists of 52 cards, with 13 each of spades, hearts, clubs, and diamonds.a. What is the
A professor has learned that three students in her class of 20 will cheat on the exam. She decides to focus her attention on four randomly chosen students during the exam.a. What is the probability
Many U.S. households still do not have Internet access. Suppose 20 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently
Consider the following cumulative probability distribution.a. Calculate P(X ‰¤ 3).b. Calculate P(X = 3).c. Calculate P(2 ‰¤ X ‰¤4)
Consider the following cumulative probability distribution.a. Calculate P(X ‰¤ 0).b. Calculate P(X = 50).c. Is this a discrete uniform distribution?Explain.
In early 2010, leading U.S. stock markets tumbled more than 2.5% as U.S. consumer confidence fell to its lowest level since August 2009 (BBC News, July 16, 2010). Given fresh economic data, an
The number of homes that a Realtor sells over a one-month period has the following probability distribution.Number of Houses Sold ... Probability0 ............ 0.301 ............. 0.502
An analyst has developed the following probability distribution of the rate of return for a common stock.a. Calculate the expected rate of return. b. Calculate the variance and the standard deviation
Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $25,000 on a clear day and $10,000 on a cloudy day.
Mark Underwood is a professor of Economics at Indiana University. He has been teaching Principles of Economics for over 25 years. Professor Underwood uses the following scale for grading.Grade
An investor considers investing $10,000 in the stock market. He believes that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will
On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes are distributed evenly on the highway.a. Find the probability of finding fewer than two
On average, 400 people a year are struck by lightning in the United States (The Boston Globe, July 21, 2008).a. What is the probability that at most 425 people are struck by lightning in a year?b.
Suppose you have an urn of ten marbles, of which five are red and five are green. If you draw two marbles from this urn, what is the probability that both marbles are red? What is the probability
A professor of management has heard that eight students in his class of 40 have landed an internship for the summer.Suppose he runs into three of his students in the corridor.a. Find the probability
The National Science Foundation is fielding applications for grants to study climate change. Twenty universities apply for a grant, and only four of them will be awarded.If Syracuse University and
Facing the worst economic climate since the dot-com bust in the early 2000s, high-tech companies in the United States search for investment opportunities with cautious optimism (USA TODAY, February
An analyst developed the following probability distribution for the rate of return for a common stock.a. Calculate the expected rate of return. b. Calculate the variance and the standard deviation of
According to the Department of Transportation, 27% of domestic lights were delayed in 2007 (Money, May 2008). At New York’s John F. Kennedy Airport, five lights are randomly selected.a. What is the
Despite the fact that home prices seem affordable and mortgage rates are at historic lows, real estate agents say they are showing more homes, but not selling more (The Boston Globe, March 7, 2009).
An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A recent report in The New York Times (November 23, 2009) suggests
According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago ( The New York Times ,
Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had
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. a. P(X 20)
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. a. P(X2.5) c. P (0 ≤ X ≤ 4)
For a continuous random variable X, P (20 X ≤ 40) = 0.15 and P(X. 40) = 0.16. Calculate the following probabilities.a. P(X< 40)b. P(X< 20)c. P(X= 40)
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)? b. What are the mean and the
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
A random variable X follows the continuous uniform distribution with a lower limit of 10 and an upper limit of 30. a. Calculate the mean and the standard deviation of the distribution. b. What is the
A random variable X follows the uniform distribution with a lower limit of 750 and an upper limit of 800. a. Calculate the mean and the standard deviation of this distribution. b. What is the
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
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
The scheduled arrival time for a daily l ight 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
You were informed at the nursery that your peach tree will definitely bloom sometime between March 18 and March 30. Assume that the bloom times follow a uniform distribution between these specified
You have been informed that the assessor will visit your home sometime between 10: 00 am and 12: 00 pm. It is reasonable to assume that his visitation time is uniformly distributed over the specified
Find the following probabilities based on the standard normal variable Z. a. P (Z >1.32) b. P (Z ≤ - 1.32) c. P (1.32 ≤ Z ≤ 2.37) d. P( -1.32 ≤ Z ≤ 2.37)
Find the following probabilities based on the standard normal variable Z.a. P (Z
Find the following probabilities based on the standard normal variable Z.a. P(-0.67 ≤ Z ≤ 20.23) b. P (0 ≤ Z ≤ 1.96) c. P(-1.28 ≤ Z ≤ 0) d. P (Z
Find the following z values for the standard normal variable Z.a. P(Z ≤ z) = 0.9744 b. P ( Z< z ) = 0.8389 c. P(- z ≤ Z ≤ z) = 0.9= d. P (0 ≤ Z ≤ z) = 0.331=
Find the following z values for the standard normal variable Z.a. P (Z ≤ z) = 0.1020 b. P (z ≤ Z ≤ 0) = 0.1772 c. P (Z< z) = 0.9929 d. P (0.40 ≤ Z ≤ z) = 0.3368
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
Assume that IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 16. Use the empirical rule for normal distributions to answer the following questions. a. What
The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. Use the empirical rule for normal distributions to answer the following
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 for normal
Let X be normally distributed with mean µ = 10 and standard deviation σ = 6. a. 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 = 4>a. 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 = 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
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
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
The random variable X is normally distributed. Also, it is known that P(X>150) 5a. Find the population mean µ if the population standard deviation σ = 15.b. Find the population mean µ if the
(Use Excel) Let X be normally distributed with µ 5 254 and σ 5 11. In addition to providing the answer, state the relevant Excel commands.a. Find P(X ≤ 266).b. Find P(250 , X , 270).c. Find
(Use Excel) Let X be normally distributed with µ = 215 and σ = 9. In addition to providing the answer, state the relevant Excel commands.a. Find P(X>212).b. Find P(0 ≤ X ≤ 5).c. Find x such
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 percentage of high
Americans are increasingly skimping on their sleep (National Geographic News, February 24, 2005). A health expert believes that American adults sleep an average of 6.2 hours on weekdays with a
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.
Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 mpg and 3.5 mpg, respectively.a. What is the
According to the company’s website, the top 25% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and
A financial advisor informs a client that the expected return on a portfolio is 8 percent with a standard deviation of 12 percent. There is a 25% chance that the return would be negative and a
A packaging system ills boxes to an average weight of 18 ounces with a standard deviation of 0.2 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd,
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,
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
The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 16 minutes and 8 minutes, respectively. a. Find the probability that a randomly
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.
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 with a mean of 25 years, calculate its
The average college student graduated with $27,200 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $7,000.a.
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
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
A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. If it is known that returns are normally distributed with a mean of
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
You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 8% with a standard deviation of 14%. The relatively less
First introduced in Los Angeles, the concept of Korean style tacos sold from a catering truck has been gaining popularity nationally (The New York Times, July 27, 2010). This taco is an interesting
A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of
While Massachusetts is no California when it comes to sun, the solar energy industry is lourishing in this state (The Boston Globe, May 27, 2012). The state's capital, Boston, averages 211.7 sunny
A certain brand of refrigerators has a length of life that is normally distributed with a mean and a standard deviation of 15 years and 2 years, respectively. In addition to providing the answer,
Assume a Poisson random variable has a mean of 6 successes over a 120-minute period.a. Find the mean of the random variable, defined by the time between successes.b. What is the rate parameter of the
Assume a Poisson random variable has a mean of four arrivals over a 10-minute interval.a. What is the mean of the random variable, defined by the time between arrivals?b. Find the probability that
A random variable X is exponentially distributed with a mean of 0.1.a. What is the rate parameter f? What is the standard deviation of X?b. Compute P (X. 0.20).c. Compute P (0.10 ≤ X ≤ 0.20).
A random variable X is exponentially distributed with an expected value of 25.a. What is the rate parameter ƛ? What is the standard deviation of X?b. Compute P(20 ≤ X ≤ 30).c. Compute P(15 ≤ X
Let X be exponentially distributed with ƛ = 0.5.In addition to providing the answer, state the relevant Excel commands.a. P(X ≤ 1)b. P(2c. P(X . 10)
Let X be exponentially distributed with µ = 1.25.In addition to providing the answer, state the relevant Excel commands.a. P(X<2.3)b. P(1.5 ≤ X ≤ 5.5)c. P(X . 7)
Studies have shown that bats can consume an average of 10 mosquitoes per minute (berkshiremuseum.org). Assume that the number of mosquitoes consumed per minute follows a Poison distribution.a. What
According to Daily Mail (February 28, 2012), there was an average of one complaint every 12 seconds against Britain's biggest banks in 2011. It is reasonable to assume that the time between
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
When crossing the Golden Gate Bridge, traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential
A hospital administrator worries about the possible loss of electric power as a result of a power blackout. The hospital, of course, has a standby generator, but it too is subject to failure, having
On average, the state police catch eight speeders per hour at a certain location on Interstate I-90. Assume that the number of speeders per hour follows the Poisson distribution. In addition to
Motorists arrive at a Gulf station at the rate of two per minute during morning hours. Assume that the arrival of motorists at the station follows a Poisson distribution. In addition to providing 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 the variance of this distribution. b.
A worker at a landscape design center uses a machine to ill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling

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