9) An item needs to go through 100 different independent processing until completion. Each process- ing...

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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.)

math Statistics-And-Probability

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Answer 1

Answer #1

Let X is a random variable shows the processing time. Here we have

E( X ) = 3. Var(X) 32

Let T is a random variable shows the completion time. Using CLT, T has approximately normal distribution with mean and SD as follows;

E(T) = 100-E(X) 300, Var(T) = 100 . Var(X) = 900

The z-score for T = 8 * 60= 480 minutes is

T- E(T) 480 300 Vvar(T)V900 UaT

The probability that item will finished in 8 hours is

P(T <= 480) = P(z <= 6) = 1.0000

Answer: 1.0000

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Answer 2

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