Practical Management Science
5th Edition
ISBN: 9781305250901
Author: Wayne L. Winston, S. Christian Albright
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 10.2, Problem 6P
Use @RISK to draw a binomial distribution that results from 50 trials with probability of success 0.3 on each trial, and use it to answer the following questions.
- a. What are the mean and standard deviation of this distribution?
- b. You have to be more careful in interpreting @RISK probabilities with a discrete distribution such as this binomial. For example, if you move the left slider to 11, you find a probability of 0.139 to the left of it. But is this the probability of “less than 11” or “less than or equal to 11”? One way to check is to use Excel’s BINOM.DIST function. Use this function to interpret the 0.139 value from @RISK.
- c. Using part b to guide you, use @RISK to find the probability that a random number from this distribution will be greater than 17. Check your answer by using the BINOM.DIST function appropriately in Excel.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
In the given problem, what other probability distributions might accurately describe Oakdale’s weekly usage of glue?
A) Why is the conditional variance a good measure of uncertainty? B) Outline the GARCH model and GARCH-M model. C) Outline one of the extensions to the basic GARCH family of models
A normally distributed population has a mean of 578 and a standard deviation of 7.50.
Find the probability that the mean of a sample of size 100 drawn from this population is between 570 and 580.
4621
0
9962
None of the other 3 answers
Chapter 10 Solutions
Practical Management Science
Ch. 10.2 - Use the RAND function and the Copy command to...Ch. 10.2 - Use Excels functions (not @RISK) to generate 1000...Ch. 10.2 - Use @RISK to draw a uniform distribution from 400...Ch. 10.2 - Use @RISK to draw a normal distribution with mean...Ch. 10.2 - Use @RISK to draw a triangular distribution with...Ch. 10.2 - Use @RISK to draw a binomial distribution that...Ch. 10.2 - Use @RISK to draw a triangular distribution with...Ch. 10.2 - We all hate to keep track of small change. By...Ch. 10.4 - Prob. 11PCh. 10.4 - In August of the current year, a car dealer is...
Ch. 10.4 - Prob. 13PCh. 10.4 - Prob. 14PCh. 10.4 - Prob. 15PCh. 10.5 - If you add several normally distributed random...Ch. 10.5 - In Problem 11 from the previous section, we stated...Ch. 10.5 - Continuing the previous problem, assume, as in...Ch. 10.5 - In Problem 12 of the previous section, suppose...Ch. 10.5 - Use @RISK to analyze the sweatshirt situation in...Ch. 10.5 - Although the normal distribution is a reasonable...Ch. 10.6 - When you use @RISKs correlation feature to...Ch. 10.6 - Prob. 24PCh. 10.6 - Prob. 25PCh. 10.6 - Prob. 28PCh. 10 - Six months before its annual convention, the...Ch. 10 - Prob. 30PCh. 10 - A new edition of a very popular textbook will be...Ch. 10 - Prob. 32PCh. 10 - W. L. Brown, a direct marketer of womens clothing,...Ch. 10 - Prob. 34PCh. 10 - Lemingtons is trying to determine how many Jean...Ch. 10 - Dilberts Department Store is trying to determine...Ch. 10 - It is surprising (but true) that if 23 people are...Ch. 10 - Prob. 40PCh. 10 - At the beginning of each week, a machine is in one...Ch. 10 - Simulation can be used to illustrate a number of...Ch. 10 - Prob. 43PCh. 10 - Prob. 46PCh. 10 - If you want to replicate the results of a...Ch. 10 - Suppose you simulate a gambling situation where...Ch. 10 - Prob. 49PCh. 10 - Big Hit Video must determine how many copies of a...Ch. 10 - Prob. 51PCh. 10 - Prob. 52PCh. 10 - Why is the RISKCORRMAT function necessary? How...Ch. 10 - Consider the claim that normally distributed...Ch. 10 - Prob. 55PCh. 10 - When you use a RISKSIMTABLE function for a...Ch. 10 - Consider a situation where there is a cost that is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.arrow_forwardBased on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)arrow_forwardWhen you use @RISKs correlation feature to generate correlated random numbers, how can you verify that they are correlated? Try the following. Use the RISKCORRMAT function to generate two normally distributed random numbers, each with mean 100 and standard deviation 10, and with correlation 0.7. To run a simulation, you need an output variable, so sum these two numbers and designate the sum as an output variable. Run the simulation with 1000 iterations and then click the Browse Results button to view the histogram of the output or either of the inputs. Then click the Scatterplot button below the histogram and choose another variable (an input or the output) for the scatterplot. Using this method, are the two inputs correlated as expected? Are the two inputs correlated with the output? If so, how?arrow_forward
- Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?arrow_forwardFederal Income Tax Returns. The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between$30,000and$60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was$16,642. Assume the standard deviation is σ=$2400. What is the probability that a sample of taxpayers from this in-come group who have itemized deductions will show a sample mean within$200 of the population mean for sample sizes 30?arrow_forwardJohnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 145 hours. The company's research department takes a sample of 90 such tubes and finds that the mean life of these tubes is 2300 hours. What is the probability that this sample mean is within 22 hours of the mean life of all tubes produced by this company? Round your answer to four decimal places. P =arrow_forward
- A GMAC MBA new-matriculants survey provided the following data for 2018 students. Excel File: data04-53.xlsx Applied to More Than One School Yes No 23 and under 207 201 24-26 299 379 Age Group 27-30 185 268 31-35 66 193 36 and over 51 169 a. Given that a person applied to more than one school, what is the probability that the person is 24 - 26 years old (to 2 decimals)? b. Given that a person is in the 36 and over age group, what is the probability that the person applied to more than one school (to 4 decimals)? c. What is the probability that a person is 24 - 26 years old or applied to more than one school (to 4 decimals)? d. Suppose a person is known to have applied to only one school. What is the probability that the person is 31 or more years old (to 4 decimals)? e. Is the number of schools applied to independent of age? Explain. Select your answer -arrow_forwardA recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. The data is provided below: Risk of Strokes Age Systolic Blood Pressure Smoker 10 59 156 0 25 65 163 0 12 60 158 0 57 86 177 1 28 59 196 0 50 76 189 1 17 57 159 1 34 78 120 1 37 80 135 1 15 78 98 0 22 71 152 1 39 70 173 1 17 67 135 0 48 77 209 1 18 60 199 0 36 82 119 1 10 66 166 0 34 80 125 1 4 62 117 0 38 59…arrow_forwardThe average weekly earnings of bus drivers in a city are $950 (that is μ) with a standard deviation of $45 (that is σ). Assume that we select a random sample of 81 bus drivers. What is the probability that the sample mean will be greater than $960? 0.99 0.66 0.023 1 Sample: n= Mean= SD= Probability[P(X>)]= z= Probability[P(Z)]= Answer: Graph:arrow_forward
- 4. ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) What is the probability that a filled bag will weigh less than 49.5 kilograms? (b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms? (c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled? (d) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?arrow_forwardFind N, mean, Standard Deviation, Probability P[X<)], Z=, Probability[P(Z<)]/Normal Distribution=, answer and graph. MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken. What is the probability that the average aptitude test score in the sample will be less than 78.69? 0.891 0 0.78 1arrow_forwardLet assume that x ̅ ~ N (50, 2) and x ~ N (50, 20), which of the two distributions above will have a narrower spread and why? 1. The population distribution because its standard deviation (2) is smaller than the other (20). 2. Both are same spread because their standard deviations are 50. 3. Both are same spread because their means are 50. 4. The sampling distribution because its standard deviation (2) is smaller than the other (20).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Single Exponential Smoothing & Weighted Moving Average Time Series Forecasting; Author: Matt Macarty;https://www.youtube.com/watch?v=IjETktmL4Kg;License: Standard YouTube License, CC-BY
Introduction to Forecasting - with Examples; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=98K7AG32qv8;License: Standard Youtube License