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.

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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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2. Suppose annual benefits for a particular item are distributed uniformly between 200 and 250. a. What's the expected value for the item's annual benefits? b. Suppose an item chosen at random gets annual benefits of $231. What percentile is this in? c. What's the likelihood of the item being profitable if its cost is $1475, its salvage value is $100, its life is 7 years, and interest is 5%?
In recent years research suggests that cell phone usage during social interactions leads to distractions, which undermines the benefits of social interaction. A recent report by greater good magazine reports that a survey shows that 82% of people report that the use of cell phones during a conversation decreases the quality and what they talk about. Assuming the greater good magazine report is accurate, and then a random sample of cell phone users during A recent conversation were sampled. You are interested in the probability that a specific number of the cell phones users would report that the use of cell phones during a conversation decreases the quality of what they talk about.
In a certain high school, the probability that a student drops out is 0.1, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25. What is the probability that a randomly selected student gets a GED?
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%
B. Answer the following: 1. MEAN OF DISCRETE RANDOM VARIABLE Find the Expected value or Mean of the following. Show your complete solution. Rafael plays a gambling game where it is possible to lose $2.00, break even, win $4.00, or win $15.00 each time he plays. The probability distribution for each outcome is provided by the following table: a. Outcome -$2.00 $0.00 0.40 $4.00 0.20 $15.00 Probability 0.30 0.10 b. Suppose that the casino decides that the game does not have an impressive enough top prize with the lower payouts, and decides to double all of the prizes, as follows: -$5.00 0.25 -$1.00 0.35 $6.00 0.25 Outcome $10.00 Probability 0.15 c. As in the case of the mean, consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. The resulting distribution is the following: -$6.00 0.30 Outcome -$3.00 $6.00 $12.00 Probability 0.40 0.20 0.10 eLea Com ASCENDENS ASIA
1.Which probability distribution would you use to calculate the probability of success or failure of Advanced Researcher's vaccine if it were to be administered to people in society?
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.
2. An actuary studied the likelihood that diff rent types of drivers would be involved in at least one collision during any one-year period. The results of the study are presented below. Probability of at least one Туре of driver Percentage of all drivers collision Teen 8% 0.15 Young adult Midlife 16% 0.08 45% 0.04 Senior 31% 0.05 Given that a driver has been involved in at least one collision in the past year, what is the probability that the driver is a young adult driver?
2. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of24 customers per hour or 0.4 customer per minute. A Assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. Use the exponential probability distribution to answer the following questions: i. What is the probability the service time is one minute or less? ii. What is the probability the service time is two minutes or less?
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?
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 27% of the nation's estimated 12.8 million undocumented immigrants. [You may find it useful to reference the z table.] a. In a sample of 50 illegal immigrants, what is the probability that more than 21% live in California? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability b. In a sample of 180 illegal immigrants, what is the probability that more than 21% live in California? (Round “z" value to 2 decimal places, and final answer to 4 decimal places.) Probability

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