1. The time between unplanned shutdowns of a power plant has an exponential dist
ID: 3154241 • Letter: 1
Question
1. The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 60 days. Find the probability that the time between two unplanned shutdowns is between 30 and 45 days.
2. The New York Times reported that the mean time to download the homepage for the Internal Revenue Service is 0.75 seconds. What is the probability that it takes you more than 2 seconds to download the page? (Use an exponential distribution to determine this probability.)
3. On average, 4 customers arrive at the drive-up window of a fast-food restaurant every 2 minutes during the lunch hour. What is the probability that the next customer will arrive within three minutes? (Use an exponential distribution to determine this probability.)
Explanation / Answer
1.
mean = u = 60
The probability between two values in an exponential distribution is
P = e^(-x2/u) - e^(-x1/u)
As
x1 = lower bound = 30
x2 = upper bound = 45
Then
P(30<x<45) = 0.134164107 [ANSWER]
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2.
mean = u = 0.75
The right tailed area in an exponential distribution is
P(x>x1) = e^(-x1/u)
As
x1 = critical value = 2
Then
P(x>2) = 0.069483451 [ANSWER]
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