Questions and Answers of Statistics For Business And Economics

Suppose you are given a die and are asked to roll the die two times and write down the numerical value that results from each roll. You are also told that you can keep rolling as long as you get a
An ornithologist is studying and recording the number of boreal owl eggs found in south-central Sweden. Is the number of eggs a discrete or continuous random variable?
As a part of the school health services offered at Alderwood Primary School, London, the weight of students are recorded. Is the weight of students a discrete or continuous random variable?
For each of the following, indicate if a discrete or a continuous random variable provides the best definition: a. The amount of oil exported by Saudi Arabia in January 2019b. The number of
After studying the queueing theory, Samara learnt that messages in a network are broken into packets that are routed to a destination server. Is the waiting time until the next packet arrives at the
List four examples of discrete random variables that could be observed in education.
List three continuous random variables that a portfolio manager at an investment firm should regularly examine.
The number of computers sold per day at Dan’s Computer Works is defined by the following probability distribution:a. P(3 ≤ x < 6) = ?b. P(x > 3) = ?c. P(x ≤ 4) = ?d. P(2 < x ≤ 5) = ?
A presidential election poll contacts 2,000 randomly selected people. Should the number of people that support candidate A be analyzed using discrete or continuous probability models?
A local grocery store has asked you to examine the probability of choosing a product based on the height of shelf on which the product is placed. The random variable X is the height of the shelf from
The Embassy of Vietnam in India receives a number of visa applications. Should the number of visas issued per day be analyzed using discrete or continuous probability models?
Consider the probability distribution function.a. Graph the probability distribution function.b. Calculate the cumulative probability distribution function.c. Find the mean of the random variable
One of the leading retail banks in China is the Postal Savings Bank of China, located in Beijing. Suppose the number of arrivals per minute at the bank, which has around 40,000 outlets, was recorded
What is the probability distribution function of the number of prime numbers when a number between 1 and 25, inclusive, is randomly selected?
Consider the probability distribution function.a. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable
The manager at a firm in Tokyo wants to organize a trip for his team in the summer of 2020, but some employees have already applied for leave. To be better prepared, he estimates the probabilities of
Let the random variable represent the number of flight delays during a day at the large airport. Prepare a table that shows the probability distribution and the cumulative probability distribution?
Amazon’s third-largest market is the United Kingdom. In 2019, the employees at a local firm in London received their salary and decided to spend a portion of it on making online purchases from
An investor is considering three strategies for a €1,200 investment. The probable returns are estimated as follows:• Strategy 1: A certain profit of €200.• Strategy 2: A profit of €12,000
For a Bernoulli random variable with probability of success P = 0.8, compute the mean and variance.
For a binomial probability distribution with P = 0.4 and n = 10, find the probability that the number of successes is equal to 5 and the probability that the number of successes is fewer than 2.
For a binomial distribution probability with P = 0.87 and n = 23, find the probability that:a. The number of successes is equal to 11.b. The number of successes is fewer than 15.
A public interest group in Belgium hires students to solicit donations by telephone. After a brief training period, the students call potential donors and are paid on a commission basis. Experience
À la Mère de Famille had opened in 1761 and is the oldest chocolate store in Paris, France. Suppose you visit the store and find that 30% of the truffles are made of white chocolate, 25% of a dark
SparkSolutions, a video surveillance systems producer in Italy, installs new security cameras and has found that for 17% of all installations, a return visit is needed to make some modifications.
The rise of cultured pearls or pearl farms have made natural pearls are very rare and have limited pearl fishing. However, a significant number of natural pearls can still be found in the Australian
A football fan is analyzing the number of people interested in purchasing tickets for Europe’s biggest football championship, the UEFA Euro 2020. The fan’s survey tells her that out of 10
A local car dealer in Germany is mounting a new cross divisional promotional campaign. Purchasers of new cases may, if dissatisfied for any reason, return the vehicle within 2 days of purchase and
A company receives a very large shipment of mobile phones. A random sample of 22 of these mobile phones will be checked, and the shipment will be accepted if only one or none of these components do
A company receives large shipments of parts from two sources. Seventy percent of the shipments come from a supplier whose shipments typically contain 10% defectives, while the remainder are from a
Determine the probability of more than 7 successes for a random variable with a Poisson distribution with parameter λ = 4.2.
Determine the probability of fewer than five successes for a random variable with a Poisson distribution with parameter λ = 9.0.
Determine the probability of fewer than or equal to five successes for a random variable with a Poisson distribution with parameter λ = 9.0.
People arrive at an ATM vestibule to withdraw cash at an average rate of two people per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be
A customer service center in India receives, on average, 2.5 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving at least 3 calls during a
A corporation has 280 personal computers. The probability that any 1 of them will require repair in a given week is 0.01. Find the probability that fewer than 3 of the personal computers will require
Compute the probability of 10 successes in a random sample of size n = 16 obtained from a population of size N = 70 that contains 24 successes.
Compute the probability of 9 successes in a random sample of size n = 25 obtained from a population of size N = 90 that contains 32 successes.
Compute the probability of 4 successes in a random sample of size n = 6 obtained from a population of size N = 30 that contains 20 successes.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for
Compute the probability of 5 successes in a random sample of size n = 12 obtained from a population of size N = 111 that contains 60 successes.
Consider the joint probability distribution:a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for
A bond analyst was given a list of 13 corporate bonds. From that list she selected 3 whose ratings she felt were in danger of being downgraded in the next year. In actuality, a total of 5 of the 13
The average amount of money a person spends on lottery tickets each month is €9. By looking at the data, a Poisson discrete distribution is assumed for this variable. Calculate each of the
Suppose the students at the University of Amsterdam, the Netherlands, are classified according their school grades (X), and the number of daily hours spent watching shows on Netflix (Y = 0 for no
Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is between 1.4 and 1.8. f(x) .5 0 0 ХО 2 x
Consider a country that imports coal and exports furniture. The value per unit of furniture exported is measured in units of thousands of euros per furniture by the random variable X. The value per
Using data from different insurance companies and their income in the member countries of the European Union (EU), a researcher claims to be able to estimate candidates faced with impending financial
Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is between 0.5 and 1.6. f(x) .5 0 0 ХО 2 x
A recent study suggested that, of all current credit users of €100,000, 6.5% either paid no penalty interest rate or paid an effective rate of less than 12%. A random sample of 100 of those
Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is less than 0.8. f(x) .5 0 0 ХО 2 x
Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is greater than 1.3. .5 Ο 0 πο 2 x
The total cost for a production process is equal to €500 plus two times the number of units produced. The mean and variance for the number of units produced are 700 and 600, respectively. Find the
A fashion house in London offers a designer a contract, according to which she is to be paid a fixed sum of £10,000 plus £1.75 for each unit of her design sold. Her uncertainty about total sales of
Let the random variable Z follow a standard normal distribution.a. Find P(Z < 1.16).b. Find P (Z >1.73).c. Find P(Z > -2.29).d. Find P(Z > -1.35).e. Find P(1.16 < Z < 1.73).f. Find
Let the random variable X follow a normal distribution with μ = 30 and σ2 = 81.a. Find the probability that X is greater than 40.b. Find the probability that X is greater than 15 and less than
Anticipated consumer demand at a restaurant for free-range steaks next month can be modeled by a normal random variable with mean 1,500 pounds and standard deviation 110 pounds.a. What is the
An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 13.5% and standard
Luca Alberti, a Hungarian florist, is considering two alternative investments. In both cases she is unsure about the percentage return but believes that her uncertainty can be represented by normal
Volvo Cars, a Swedish luxury vehicles company, purchases computer process chips from two suppliers, and the company is concerned about the percentage of defective chips. A review of the records for
Scores on an economics test follow a normal distribution. What is the probability that a randomly selected student will achieve a score that exceeds the mean score by more than 1.5 standard
A new television series is to be shown. A broadcasting executive feels that his uncertainty about the rating that the show will receive in its first month can be represented by a normal distribution
The number of hits per day on the Web site of E-CommEx, Inc., is normally distributed with a mean of 510 and a standard deviation of 140.a. What proportion of days has more than 620 hits per day?b.
Given a random sample size of n = 9 0 0 from a binomial probability distribution with P = 0.30 do the following:a. Find the probability that the number of successes is greater than 305.b. Find the
Given a random sample size of n = 4,900 from a binomial probability distribution with P = 0.50 do the following:a. Find the probability that the number of successes is greater than 2,545.b. Find the
Avis Rent, a South African car-rental company, has determined that the probability a car will need service work in any given month is 0.15. Avis Rent has 1200 cars.a. What is the probability that
It is known that 10% of all the items produced by a particular manufacturing process are defective. From the very large output of a single day, 100 items are selected at random.a. What is the
A random sample of 200 blue-collar employees at Ricci S.p.A, an Italian construction company, is surveyed to assess their attitudes toward a proposed new work schedule. If 65% of all blue-collar
Suppose St. Vincent’s Hospital Melbourne, Australia, finds that 30% of its accounts are at least 1 month in arrears. A random sample of 500 accounts was taken.a. What is the probability that fewer
The tread life of tires from Nokian Tyres, a Finnish automobile company, can be modeled by a normal distribution with a mean of 35,000 miles and a standard deviation of 5,000 miles. A sample of 200
Given an arrival process with λ = 0.6, what is the probability that an arrival occurs in the first t = 8 time units?
Times to gather preliminary information from arrivals at an outpatient clinic follow an exponential distribution with mean 15 minutes. Find the probability, for a randomly chosen arrival, that more
It is known that for a laboratory computing system the number of system failures during a month has a Poisson distribution with a mean of 0.8. The system has just failed. Find the probability that at
Swapna David is a customer assistant consultant for Acme Information Systems, who provides assistance for computer users. The mean number of calls per hour is 30 from across Europe and calls are
A random variable X is normally distributed with a mean of 144 and a variance of 144, and a random variable Y is normally distributed with a mean of 150 and a variance of 225. The random variables
A random variable X is normally distributed with a mean of 64 and a variance of 64, and a random variable Y is normally distributed with a mean of 160 and a variance of 256. The random variables have
A random variable X is normally distributed with a mean of 500 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables
A consultant is beginning work on three projects. The expected profits from these projects are €65,000, €83,000, and €57,000. The associated standard deviations are €12,500, €17,200, and
Ten inspectors are employed by Norway’s Kitron Group to check the quality of components produced on an assembly line. For each inspector the number of components that can be checked in a shift can
It is estimated that in normal highway driving, the number of miles that can be covered by automobiles of a particular model on 1 gallon of gasoline can be represented by a random variable with mean
Aircon, a South African company, services home air conditioners. It is known that times for service calls follow a normal distribution with mean of 50 minutes and a standard deviation of 12
It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 120 minutes and a standard deviation of 40 minutes.a. What is the
Pizza EATaliano, a pizzeria in Budapest, delivers to residents of Vécsey street, Budapest. Delivery times follow a normal distribution with a mean of 30 minutes and a standard deviation of 6
A online video store in the United Kingdom estimates that annual expenditures of members on rentals follow a normal distribution with a mean of £150. It was also found that 20% of all members spend
It is estimated that amounts of money spent on gasoline by customers at a gas station in Bristol, England, follow a normal distribution with a standard deviation £3.4. It is also found that 5% of
An organization that gives regular seminars on sales motivation methods determines that 55% of its clients have attended previous seminars. From a sample of 500 clients what is the probability that
A market research organization has found that 45% of all supermarket shoppers refuse to cooperate when questioned by its pollsters. If 1,500 shoppers are approached, what is the probability that
Helicopteros Sanitarios, an ambulance service in Fuengirola, Spain, receives an average of 20 calls per day during the time period 6 p.m. to 6 a.m. for assistance. For any given day what is the
A fish market in Phnom Penh, Cambodia, offers a large variety of fresh fish on its stands. You want to prepare the popular Khmer dish called amok and found that the average chunk of catfish, one of
A Godiva Chocolate Shop in Germany offers different sizes and weights of boxes of truffles. a. Find the probability that a box of truffles weighs between 300 and 305 grams. The mean weight of a
A population contains two million 0s and nine million 1s. What is the approximate sampling distribution of the sample mean in each of the following cases?a. The sample size is n = 4b. The sample size
Given a population with a mean of μ = 105 and a variance of σ2 = 16, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 25 is obtained.a. What are the
Given a population with a mean of μ = 150 and a variance of σ2 = 1,600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 36 is obtained.a. What
Given a population with a mean of μ = 104 and a variance of σ2 = 81, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 25 is obtained.a. What are the
When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 105 and a standard deviation of 20. A random sample of 25 different
The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 21 and a standard deviation of 5. The population distribution can be assumed to be normal. A random sample
The price-earnings ratios for all companies whose shares are traded on the Tokyo Stock Exchange follow a normal distribution with a standard deviation of 3.5. A random sample of these companies is
A chain of coffee shops, BeanBoy, is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and BeanBoy wishes to

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