An item needs to go through 100 different independent processing until completion. Each processing takes exponential...
An item needs to go through 100 different independent processing until completion. Each processing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)
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An item needs to go through 100 different independent processing
until completion. Each processing takes exponential...
9. An item needs to go through 100 different independent processing until completion. Each process- ing...
9. An item needs to go through 100 different independent processing until completion. Each process- ing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)
9) An item needs to go through 100 different independent processing until completion. Each process- ing...
9) An item needs to go through 100 different independent processing until completion. Each process- ing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)
You have 100 light bulbs whose lifetimes are modeled by an independent exponential distribution with a...
You have 100 light bulbs whose lifetimes are modeled by an independent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately with a new one. Use the central limit theorem to approximate the probability that there is still a working bulb between 790 hours and 820 hours
Suppose a worker needs to process 200 items. The time to process each item is exponentially...
Suppose a worker needs to process 200 items. The time to process each item is exponentially distributed with a mean of 1 minutes, and the processing times are independent. Approximately, what is the probability that the worker finishes in less than 5 hours?
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled...
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled by an indepen- dent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately by a new one. i. (5 pointsUse the central limit theorem to approximate the probability that there is still a working bulb after 850 hours. ii. (5 points) Use the central limit theorem to approximate the probability...
Question 3 (10 points) You've invited 100 guests to a dinner party where the only item...
Question 3 (10 points) You've invited 100 guests to a dinner party where the only item on the menu are shawarma sandwiches! Let X; (where 1<i< 100 denote the number of shawarma sandwiches the i-th guest consumes at the party. Suppose you believe that X; = 0,1, or 2 with probability 1/10,8/10, and 1/10 respectively (for 1<i<100). Suppose you also believe that the number of shawarma sandwiches each guest consumes is independent from the number of shawarma sandwiches other guests...
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with...
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with mean 1. Let 100 k=1 (a) Rccall, Markov's incquality is P(Y > a) for a> 0 Using Markov's inequality, estimate the probability that P(Y > 120). (b) Rccal, Chebyshev's incquality is Using Chebyshev's inequality, estimate P( Y-?> 20) (c), (d) Using the Central Limit Theorem, estimate P(Y > 120) and Ply-? > 20).
The time it takes me to go shopping follows an exponential distribution with a mean of...
The time it takes me to go shopping follows an exponential distribution with a mean of 30 minutes. What is the probabil ity that I finish shopping in 40 minutes or less? Round to the nearest decimal! 73.6% 62.3% 77,7% 75.3% None of the above What is the probability that it takes me between 40 and 50 minutes to finish my shopping? Round to the nearest decimal! O 14.1% 10.6% 7.5% 81.1 % None of the above If the per...
Assume that for this project to be completed, five independent tasks must be completed. These tasks...
Assume that for this project to be completed, five independent tasks must be completed. These tasks are proceeding in parallel by five different subcontractors. To keep it simple, let's assume that each task takes between 1 and 5 months to complete (uniformly distributed, i.e. equally likely to take any amount of time between 1 and 5 months). So, the mean time to complete each task is 3 months and the probability of any given task taking 3 months or longer...
More than 100 million people around the world are not getting enough sleep; the average adult...
More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye. A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) 6.9 hours and SD(X)-1.2 hours. Question 1. Find the probability...
9. An item needs to go through 100 different independent processing until completion. Each process- ing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)
9) An item needs to go through 100 different independent processing until completion. Each process- ing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)
You have 100 light bulbs whose lifetimes are modeled by an independent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately with a new one. Use the central limit theorem to approximate the probability that there is still a working bulb between 790 hours and 820 hours
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled by an indepen- dent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately by a new one. i. (5 pointsUse the central limit theorem to approximate the probability that there is still a working bulb after 850 hours. ii. (5 points) Use the central limit theorem to approximate the probability...
Question 3 (10 points) You've invited 100 guests to a dinner party where the only item on the menu are shawarma sandwiches! Let X; (where 1<i< 100 denote the number of shawarma sandwiches the i-th guest consumes at the party. Suppose you believe that X; = 0,1, or 2 with probability 1/10,8/10, and 1/10 respectively (for 1<i<100). Suppose you also believe that the number of shawarma sandwiches each guest consumes is independent from the number of shawarma sandwiches other guests...
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with mean 1. Let 100 k=1 (a) Rccall, Markov's incquality is P(Y > a) for a> 0 Using Markov's inequality, estimate the probability that P(Y > 120). (b) Rccal, Chebyshev's incquality is Using Chebyshev's inequality, estimate P( Y-?> 20) (c), (d) Using the Central Limit Theorem, estimate P(Y > 120) and Ply-? > 20).
The time it takes me to go shopping follows an exponential distribution with a mean of 30 minutes. What is the probabil ity that I finish shopping in 40 minutes or less? Round to the nearest decimal! 73.6% 62.3% 77,7% 75.3% None of the above What is the probability that it takes me between 40 and 50 minutes to finish my shopping? Round to the nearest decimal! O 14.1% 10.6% 7.5% 81.1 % None of the above If the per...
More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye. A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) 6.9 hours and SD(X)-1.2 hours. Question 1. Find the probability...
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