Concept explainers
(a)
Calculate the mean and standard deviation.
(a)
Explanation of Solution
The probability distribution of the random variable X is shown below:
Table 1
X | 0 | 1 | 2 | 3 |
P(X) | 0.4 | 0.3 | 0.2 | 0.1 |
The mean value of the probability distribution of X is calculated as follows:
The mean value is 1.
The standard deviation of probability distribution of X is calculated as follows:
The standard deviation is 1.
Probability distribution: The probability distribution shows the probabilities of incidence of different likely outcomes in a test.
(b)
The probability distribution of Y.
(b)
Explanation of Solution
The probability distribution of Y where
X | 0 | 1 | 2 | 3 |
Y | 2 | 5 | 8 | 11 |
P(Y) | 0.4 | 0.3 | 0.2 | 0.1 |
(c)
The mean and variance of Y.
(c)
Explanation of Solution
The mean value of the probability distribution of Y is calculated as follows:
The mean value is 5.
The standard deviation of the probability distribution of Y is calculated as follows:
The standard deviation is 3.
(d)
The mean, variance, and standard deviation.
(d)
Explanation of Solution
The mean value is calculated as follows:
The mean value is 5.
Variance and standard deviation are calculated as follows:
The variance is 9 and standard deviation is 3. The parameters are identical.
Want to see more full solutions like this?
Chapter 7 Solutions
Statistics for Management and Economics (Book Only)
- 1. The following table gives the PDF (Probability Density Function) of the discrete variable X X -1 -2 2 3 4 f(x) 0.1 0.2 0.1 0.3 0.1 0.2 Calculate the E(x) (expectation) and var(x) (variance) 2. Prove the following properties of expectation and variance: If a and b are constants, X and Y are random variables, then E(aX+b)=aE(x)+b var (aX+ b) = a² var (X) var (X+ Y)= var (X) + var (Y) +2 cov(X, Y) =var (X) + var (Y) + 2pox0y Of which p is correlation coefficient, oz and o, are standard error of X and Y. 3. Assume that X- N(6, 4). What is the probability that 2 10?arrow_forward1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.arrow_forwardA call center in Perth, Australia receives an average of 1.3 calls per minute. By looking at the date, a Poisson discrete distribution is assumed for this variable. Calculate each of the following.a. The probability of receiving no calls in the first minute of its office hours.b. The probability of receiving 1 call in the first minute.c. The probability of receiving 3 calls in the first minute.arrow_forward
- A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with a mean of 20 minutes and a standard deviation of 4 minutes.a. What is the probability that a delivery will take between 15 and 25 minutes?b. The service does not charge for the pizza if delivery takes more than 30 minutes. What is the probability of getting a free pizza from a single order?c. During final exams, a student plans to order pizza five consecutive evenings. Assume that these delivery times are independent of each other. What is the probability that the student will get at least one free pizza?d. Find the shortest range of times that includes 40% of all deliveries from this service.e. For a single delivery, state in which of the following ranges (expressed in minutes) the delivery time is most likely to lie.18-20, 19-21, 20-22, 21-23f. For a single delivery, state in which of the following ranges (expressed in minutes) the delivery time is least likely to lie.18-20,…arrow_forwardQuestion 15 Suppose X is a random variable taking values 0, 1, 2, 3, 4, 5 with equal probability. What is the variance of X?arrow_forwardusing 'standard Normal Table ' , calculate the following probabilities. 1. Pr(z < -1.12) 2. Pr(z >2.32) 3.pr(1.22 < z >2.53) 4.pr(-3.22 < z < 0.22) 5.pr(-2.36 < z < -0.50)arrow_forward
- A car salesperson estimates the following probabilities for the number of cars that she will sell in the next week: Number of cars 0 1 2 3 4 5 Probability 0.10 0.20 0.35 0.16 0.12 0.07 a. Find the expected number of cars that will be sold in the week.b. Find the standard deviation of the number of cars hat will be sold in the week. c. The salesperson receives a salary of $250 for the week, plus an additional $300 for each car sold. Find the mean and standard deviation of her total salary for the week. d. What is the probability that the salesperson’s salary for the week will be more than $1,000?arrow_forwardA university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course a. Compute the probability that 2 or fewer will withdraw (to 4 decimals). b. Compute the probability that exactly 4 will withdraw (to 4 decimals). c. Compute the probability that more than 3 will withdraw (to 4 decimals). d. Compute the expected number of withdrawals.arrow_forwardOn average a supermarket sells 500 litres of milk a day with a standard deviation of 50 litres. If the supermarket has 600 litres in stock at the beginning of a day, what is the probability that it will run out of milk? What is the probability that demand is between 450 and 600 litres in a day? How many litres should the supermarket stock if it wants the probability of running out to be 0.05? 4. How many should it stock if it wants the probability of running out to be 0.01?arrow_forward
- Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #arrow_forwardAirline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a 15-second period (to 4 decimals). d. Compute the probability of at least one arrival in a 15-second period (to 4 decimals).arrow_forwardSuppose that the distribution of Uber rides around the quoted arrival time is normally distributed. Themean waiting time (relative to the quoted time) is 0, with a standard deviation of 3 minutes.a. Using the empirical rule, what percentage of rides arrive within 3 minutes of the mean (3 minutesbefore to 3 minutes after)?b. Graphically depict the area that would need to be calculated to determine the probability ofwaiting more than 4 minutes for a ride. Explain your graph.arrow_forward
- Principles of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSON
- Principles of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-...EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education