1) The arrival time of an elevator in a 12-story dormitory is equally likely at
ID: 3254663 • Letter: 1
Question
1)
The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 5.5 minutes.
What is the probability that an elevator arrives in less than 2.6 minutes? (Round intermediate calculations to 4 decimal places and final answer to 3 decimal places.)
What is the probability that the wait for an elevator is more than 2.6 minutes? (Round intermediate calculations to 4 decimal places and final answer to 3 decimal places.)
2)
A random variable X follows the uniform distribution with a lower limit of 750 and an upper limit of 850.
Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.)
What is the probability that X is less than 840? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 5.5 minutes.
Explanation / Answer
(1)
(a) Mean = (0 + 5.5)/2 = 2.75
(b) P(x < 2.6) = (2.6 - 0)/(5.5 - 0) = 0.473
(c) P(x > 2.6) = 1 - 0.473 = 0.527
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