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statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Again consider the car sales rep in question 67. What is the probability that she will make exactly two sales after speaking to four customers?Question 67A car sales representative sees an average of
What is the probability that the number X of successes in the personnel manager’s sample of 100 employees in question 10 will be 48 or more?
A battery producer invents a new product. The life of the new battery is found to follow a normal distribution with a mean of 72 months and a standard deviation of 12 months. The producer guarantees
A car manufacturer designs a fuel-efficient car for 1993. The company argues that the car can attain an average of 45 miles per gallon. The miles per gallon of the car follows a normal distribution
You work for a furniture factory that procures springs from an outside supplier.Every month, a truckload of springs comes in. From each shipment, you randomly inspect 400 springs. If there are 10 or
A consumer rights organization wants to find out whether a local dairy farm actually puts 16 oz of milk into the container that is labeled 16 oz. Assume the milk put into the container by the local
A name-brand TV dinner boasts that its pot roast has no more than 120 calories per serving. Suppose 95% of the servings of this product actually contain fewer than 120 calories. Find the probability
The Food and Drug Administration randomly tests 1,000 of a certain brand of cigarettes to see whether the nicotine content reaches a dangerous level. If 20 or more cigarettes contain more nicotine
The light bulbs produced by Edison Lighting Corporation last an average of 300 h. The life of the light bulbs is believed to follow a normal distribution with a standard deviation of 10. A customer
The number of phone calls that reach 1–800 numbers in a certain time period follows a Poisson distribution. Assume that there are about 15,000 potential callers. Each caller has a probability of
A camcorder is sold with a 1-year warranty. The probability that a camcorder is brought back for service under the warranty is 2 %. It costs the manufacturer$20 on average to repair a camcorder
What are the advantages of using the lognormal distribution over using the normal distribution to describe stock prices?
Suppose that X is distributed as normal with a mean of 5 and a standard deviation of 2. Compute the standard normal values of X, given the following values of X: (a) 3 (b) 2 (c) 9 (d) 11 (e) 6 (f) 10
Use the standard normal values you computed in question 30, and find the probability that Z is less than those values.Question 30Suppose that X is distributed as normal with a mean of 5 and a
Calculate the area under the normal curve between the following: (a) z = 0 and z = 2.0 (b) z = 3.5 and z = - (c) z = 1.2 and z = 3 (d) z - 1 1.3 and z = 1.3 1 and z = 1 (e) z = (f) z = 3 and z = 4
Find the value for z0 for the following probabilities: (a) P(Z > Zo) = .10 (b) P(Z > Zo) = .75 (c) P(-Zo
Suppose that X is normally distributed with a mean of 5 and a standard deviation of 2. Find the following probabilities: (a) X is between 5 and 9. (b) X is between 0 and 8. (c) X is greater than 6.
Briefly explain why it is useful for us to be able to approximate the binomial and Poisson distributions by using a normal distribution. Explain how we make this approximation.
Use the normal approximation to the binomial distribution with n = 100 and p = .3.(a) What is the probability that a value from the binomial distribution will have a value greater than 35?(b) What is
Use the normal approximation to the binomial distribution with n = 500 and p = .7.(a) What is the probability that a value from the binomial distribution will have a value greater than 325?(b) What
Use the normal approximation to the Poisson distribution with λ = 75.(a) What is the probability that a value from the Poisson distribution will be greater than 50?(b) What is the probability that a
The time a customer waits for service at a bank is distributed normally with a mean of 4 min and a standard deviation of 1 min. Compute the probability that a customer must wait for:(a) More than 10
The time it takes to get a car’s oil changed at Speedy Lube is distributed normally with a mean of 12 min and a standard deviation of 2 min. Compute the probability that a customer will have her or
A quality control manager has determined that the number of defective light bulbs in a case of 1,000 follows a normal distribution with a mean of 10 and a standard deviation of 3. Compute the
A survey of recent masters of business administration (MBAs) reveals that their starting salaries follow a normal distribution with mean $48,000 and standard deviation $9,000. Find the probability
Use the Black–Scholes option pricing formula to compute the value of a call option, given the following information: S = $55 X = $50 r = .065 t = .5 0.25 Price of stock Exercise price Risk-free
Answer question 43 again for an option with an exercise price of $55. How does the exercise value of the call option affect the option’s price?Question 43Use the Black–Scholes option pricing
Answer question 43 again for an option with t = .3 years. How does the time until the option expires affect the value of the call option?Question 43Use the Black–Scholes option pricing formula to
Answer question 43 again for an option whose stock price is $60. How does the price of the stock affect the value of the call option?Question 43Use the Black–Scholes option pricing formula to
Answer question 43 again when r = .10. How does a change in the risk-free rate of interest affect the value of the call option?Question 43Use the Black–Scholes option pricing formula to compute the
Answer question 43 again when σ2 = .50. How does a change in the variance of the stock’s return affect the value of the call option?Question 43Use the Black–Scholes option pricing formula to
Draw a standard normal probability function and show the area under the curve for(a) Plus or minus one standard deviation from the mean(b) Plus or minus two standard deviations from the mean(c) Plus
A company has a mean earnings per share (EPS) of $3.25 with a standard deviation of $1.21. Assume that the earnings are normally distributed. Compute the probability that EPS will be:(a) Between
An investment analyst is following the stock of High Flyer Company. She believes that in any month, the stock has a 65 % chance of going up and a 35 %chance of going down. Using the binomial
A gas station finds that the mean number of people buying gas in any 30-min period is 16. Use the Poisson distribution to compute the probability that between 25 and 35 people, inclusive, will buy
Calculate ey for the following values of y: (a) y = 1 (b) y = 5 (c) y = -.5 (d) y = -2.5 (e) y = 3.1 (f) y = - I (g) y = .05 (h) y = .32 (i) y = 6.1 (j) y = -5.4
Suppose x = ey. Compute the value of y, given the following values of x: (a) x = 2 (b) x = 3 (c) x ~ 1.5 (d) x 3 (e) x = .5 (f) x = .002 (g) x = 10 (h) x = 1
Briefly explain what a cumulative distribution function is. Give some examples of occasions when the cumulative distribution function is useful.
A quality control manager has found that the mean number of ounces of cereal in a 16-oz box is 16 oz with a standard deviation of 2 oz. Calculate the probability that a randomly selected box of
An investment analyst calculates that the mean price of gold is $392 per ounce with a standard deviation of $12. Assume the price of gold follows a normal distribution. Compute the probability that
You know that a certain stock’s dividend yield has a mean of 6 % and a standard deviation of 2 %. Assume the dividends follow a normal distribution.Compute the probability that the dividend yield
Use the Black–Scholes option pricing formula to compute the value of a call option, given the following information: S = $105 X = $110 r = .055 t=.9 o = .45 Price of stock Exercise price Risk-free
The number of claims filed each week with Security Insurance Company has a mean of 700 and a standard deviation of 250. Calculate the probability that the number of claims this week will be:(a)
From past history, we know that 60 % of people audited by the IRS owe money to the government. If we take a random sample of 500 people who are being audited, what is the probability that between 280
The probability is .1 that a customer entering a food store will buy a can of coffee. If 1,000 customers enter the store, what is the minimum number of cans of coffee the store must have on hand to
Determine the following probabilities. Assume that X follows a normal distribution: (a) P(80 X 951 =92, o = 10) (b) P(X> 150 = 99, o = 25)
A public library has observed that the fine for overdue books is approximately normally distributed with a mean of $2.72 and a standard deviation of $.37.(a) What is the probability that a fine will
The breaking strength for paper bags used in a grocery store is approximately normally distributed with a mean of 15 lb and a standard deviation of 2 lb.(a) What proportion of these bags has a
A newspaper publisher has mean sales of 28,200 copies per day with a standard deviation of 3,100. If the publisher distributes 32,000 copies of the paper to the newsstands, what is the probability
Value Line ranks 1,700 stocks according to their timeliness and riskiness. In other words, Value Line classifies these 1,700 stocks into five ranks (groups) on the basis of their return potential and
The following MINITAB output displays the cumulative distribution function curves of three normal distributions. Their mean and variance, respectively, are (0, .5), (0, 1), and (0, 2). Please compare
The following MINITAB output exhibits the cumulative distribution function curves of three lognormal distributions. Their mean and variance, respectively, are (1, .5), (1, 1), and (1, 2). Compare the
The monthly earnings of financial analysts are normally distributed with a mean of $5,700. If only 6.68 % of the financial analysts have a monthly income of more than $6,140, what is the value of the
Suppose 15 % of the parts produced by a machine are defective. Use a normal approximation to the binomial distribution. What is the probability that a sample of 50 parts contains:(a) Five or more
Suppose the grades of students were normally distributed with a mean of 73 and a standard deviation of 15.(a) If 10 % of her students failed the course and received Fs, what was the maximum score
A local bank has determined that the daily balances X of the checking accounts of its customers are lognormally distributed with an E(lnX) = $5.5 and Var(lnX) = 1.5.(a) What percentage of its
Suppose Y represents the number of times a homemaker stops by the local convenience store in a week. The probability distribution of Y follows. Find the expected value and variance of Y. y 0 1 2 3 4
The managers of a grocery store are interested in knowing how many people will shop in their store in a given hour. Suppose they collect data and find that the average number of people who enter the
Suppose you are tossing a fair coin 20 times. What is the probability that you will toss exactly five heads? What is the probability that you will toss five or fewer heads?
Calculate the mean and variance for the distribution given in question 49.Question 49Suppose you are tossing a fair coin 20 times. What is the probability that you will toss exactly five heads? What
You are rolling a six-sided fair die eight times. What is the probability that you will roll exactly two sixes? What is the probability that you will roll two or fewer sixes?
Calculate the mean and variance for the distribution given in question 51.Question 51You are rolling a six-sided fair die eight times. What is the probability that you will roll exactly two sixes?
Doctors at the Centers for Disease Control estimate that 30 % of the population will catch the Tibetan flu. What is the probability that in a sample of 10 people, exactly three will catch the flu?
Answer question 57 when X = $95. How does a change in the exercise price affect the value of the call option?Question 57You are given the following information about a stock:Calculate the value of
Answer question 57 when S = $110. How does a change in the value of the stock affect the value of the call option?Question 57You are given the following information about a stock:Calculate the value
Answer question 57 again, finding the value of the option if the stock goes up in 4 out of the 5 months.Question 57You are given the following information about a stock:Calculate the value of the
Suppose a box is filled with 25 white balls and 32 red halts. Find the probability of drawing six red balls and four white balls in 10 draws without replacement.
Redo question 63 with replacement.Question 63Suppose a box is filled with 25 white balls and 32 red halts. Find the probability of drawing six red balls and four white balls in 10 draws without
You are drawing five cards from a standard deck of cards with replacement.You win if you draw at least three red cards in five draws. What is the probability of your winning?
Two tennis players are playing in a final-set tie breaker. Player A is considered to have a 70–30 % edge over player B. The player who wins seven of 13 points will win the championship. What is the
A car sales representative sees an average of four customers in a day. Each time she talks to a customer, she has a 25 % chance of making a deal. What is the chance that she will make four deals
The following test is given to people who claim to have extrasensory perception(ESP). Five cards with different shapes on them are hidden from the person. A card is randomly drawn, and the person is
Again consider the test in question 70. What is the probability that a person taking the test will get eight out of 20 correct? Do you believe that a person who gets eight out of 20 correct has
(a) Use the monthly rates of return for both GM and Ford listed in Fig. 6.11 to calculate the correlation coefficient between the monthly rates of return for these two companies.(b) Using the results
Say we toss two six-sided dice and let the random variable be the total number of dots observed.(a) Calculate both the probability and the cumulative probability distributions.(b) Draw a graph
The following table exhibits the monthly rate of return of S&P 500 and American Express. Use the MINITAB program to:(a) Calculate the mean and standard deviation of both returns.(b) Calculate the
A production process produces 0.05 % defective parts. A sample of 10,000 parts from the production is selected. In(a) and (b), what is the probability that:(a) The sample contains exactly two
The results of a survey of married couples and the number of children they had are shown below.Determine the expected number of children and the standard deviation for the number of children. Number
The average number of calls received by an operator in a 30-min period is 12.(a) What is the probability that between 17:00 and 17:30 the operator will receive exactly eight calls?(b) What is the
In a lot of 200 parts, 50 of them are defective. Suppose a sample of 10 parts is selected at random, what is the probability that two of them are defective? What is the expected number of defective
A study indicates that an assembly line task should take an average of 3.20 min to complete, with a standard deviation of 0.75 min. What is the probability that the task will take between 1.80 and
Indicate whether each of the following random variables is continuous or discrete.(a) The time it takes a mechanic to service a car.(b) The number of new housing starts in New Jersey this year.(c)
The random variable Z is normally distributed with a mean of μz = 0 and a standard deviation of σz = 1. Find the following probabilities: (a) P(Z 1.65) (b) P(Z> -2.38) (c) P(Z> 2.95) (d) P(Z <
The random variable Z is normally distributed with μz = 0 and σz = 1. Find the following values of b: (a) P(Z < b) = .9280 (b) P(Z b) = .9949 (c) P(Z> b) = .0074 (d) P(Z
A random variable X is normally distributed with μX = 5 and σX = 2.7. Find the following probabilities, using both manual calculations and the MINITAB program: (a) P(X < 7.40) (b) P(X> -1.50)
The random variable Y is normally distributed with μY = 28.00 and σY = 10.Find the following values of b: (a) P(Y b) = .8106 (c) P(Y> b) = .0099 (d) P(Y
The following table gives the amount of time X, in seconds, by which an automated manufacturing process misses the designed completion time when performing a certain task. Negative values indicate
Suppose that 35 % of the employees of the Harrison Company belong to unions. To determine union members’ attitudes toward management, the company’s personnel manager takes a random sample of 100
Suppose that a batch of n = 80 items is taken from a manufacturing process that produces a fraction p = .16 of defectives. What is the probability that this batch will contain between 19 and 20
The IQ scores of human beings are scaled to follow a normal distribution with mean 100 and standard deviation 16. If those with IQ scores higher than 154 are regarded as geniuses, how many geniuses
A college professor teaches corporate finance every semester. The tests for the course are standardized so that the test scores exhibit a normal distribution with a mean of 75 and a standard
Suppose that X represents the number of cars arriving at a toll booth in 1 min.Further, suppose that X can assume the values 1, 2, 3, 4, and 5 and has the following distribution:Calculate the
The manager in the local bank discovers that people come in to cash their paychecks on Friday. The amount of money withdrawn on Friday follows a normal distribution with 5 million as the mean and 1
A local bakery found that it was throwing out too many cookies every night, so the manager conducted a study on the sales of cookies and found that on an ordinary day, the sales of cookies follow a
A soft drink producer has just installed a new assembly line. The assembly line is adjusted to dispense an average of 12.05 oz of soda into the 12-oz soda can with a standard deviation of .02. What
In question 17, what is the probability that 2 cans out of a six pack will contain less than 12 oz?Question 17A soft drink producer has just installed a new assembly line. The assembly line is
In question 17, the average amount of soda dispensed into the cans is adjustable. If we want to make sure that 99.9 % of the soda cans contain more than 12 oz, to what should we adjust the
A golfer enters a long-driving contest in which he wins if he drives the golf ball 300 yards or more and loses if he drives it less than 300 yards. Assume that every time he hits a golf ball, he has
A phone marketing company knows that the number of people who answer the phone between 10:00 and 10:15 a.m. has a Poisson distribution. The average number is eight. What is the probability that the
A market survey shows that 75 % of all households own a VCR. Suppose 100 households are surveyed.(a) What is the probability that none of the households surveyed owns a VCR?(b) What is the

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