Problem 6You're a production engineering manager at a producer of pumpkin spice coffee. You're lookinginto failures of one of the coffee bagging machines, and historical data suggests that themachine fails on average 7.2 times per month and that failures per month follow a Poissondistribution.a. What is the probability that the machine fails at least five times next month?b. You're looking into replacing the bagging machine with one that fails on average 4.1times per month. What is the probability that the machine fails at least five times nextmonth?c. The new machine costs $12,000. Assuming the machines are identical except for failurerate (i.e., no additional productivity), how long would it take to pay off on averagethrough reduced failures when the average cost of a machine failure is $165.

Answered: Image /qna-images/answer/6abb9792-5fbc-4f72-9bfe-9a57617f1b83.jpg

Answered: You're a production engineering manager…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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For each of the following situations, first determine whether you should use the normal or binomial distribution to answer the questions. Next, answer the question posed: 1) According to the AAA (American Automobile Association) in April 20, 2005, a family of two adults and two children on vacation in the United States will pay an average of $247.02 per day for food and lodging with a standard deviation of $60.41 per day. What is the probability that the daily expenses are over $250 per day?
4. An IT department at a small business has 9 laptop computers and 18 desktop computers. The research group is allocated twelve computers. a. What is the probability that the research department will obtain exactly 8 laptops? b. What is the expected value of the distribution of the number of laptops obtained? c. What is the variance of the distribution of the number of laptops obtained?
5. Emergency patients arrive at a dental surgery at a mean rate of one every 2 hours. Calculate the probability that such a patient arrives within the next 1.5 hours. The surgery manager wants to avoid the arrival of two such patients within one half-hour period. Calculate the probability of this event happening.
In the month of July, the average electrical Eversource bill in Amherst Massachusetts is $72 with a standard deviation of $6. Suppose that the electrical bills are normally distributed, what is the probability that the average electrical bill in Amherst for 15 residents is less than $75? Select one: A. 78.45% B. 23.27% C. 97.38% D. 31.21%
1. True or False a. p-values are used to determine statistical significance. b. If two events are positively correlated, then one of them must have caused the other. c. If two variables are negatively correlated, then one of them tends to decrease as the other increases.
Much is made of the fact that certain mutual funds outperform the market year after year (that is, the return from holding shares in the mutual fund is higher than the return from holding a portfolio such as the S&P 500). For concreteness, consider a 10-year period and let the population be the 4,170 mutual funds reported in The Wall Street Journal on January 1, 1995. By saying that performance relative to the market is random, we mean that each fund has a 50–50 chance of outperforming the market in any year and that performance is independent from year to year. (i) If performance relative to the market is truly random, what is the probability that any particular fund outperforms the market in all 10 years? (ii) Of the 4,170 mutual funds, what is the expected number of funds that will outperform the market in all 10 years? (iii) Find the probability that at least one fund out of 4,170 funds outperforms the market in all 10 years. What do you make of your answer? (iv) If you have a…
Body temperature. Suppose the body temperature of healthy individuals is approximately normally distributed with a mean of 37.0°C and a standard deviation of 0.4°C. a. If 130 healthy individuals are randomly selected, what is the probability that the average temperature for these individuals is 36.80°C or lower? b. Would you consider an average temperature of 36.80°C as unlikely to occur if the true average temperature of healthy individuals is 37.0°C?
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. 39.9 40.6 41.3 42 42.7 43.4 44.1 inches O -2.1-1.4 -0.7 0 0.7 1.4 2.1 inches O 10 14 18 22 26 30 34 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) 0.8490 X inches 19.9 20.6 21.3 22 22.7 23.4 24.1 inches
Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed. a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days. b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below. 4641056443743774 SAMPLE MEAN =? SAMPLE STANDARD DEVIATION =? c. Using the results of part (b), determine what type of test is…

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