A bus comes by every 7 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 7 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible.The mean of this distribution is The standard deviation is The probability that the person will wait more than 1 minutes is Suppose that the person has already been waiting for 0.7 minutes. Find the probability that the person's total waiting time will be between 2.2 and 3.9 minutes 90% of all customers wait at least how long for the train?  minutes.

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Asked Nov 23, 2019
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A bus comes by every 7 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 7 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible.

  1. The mean of this distribution is 
  2. The standard deviation is 
  3. The probability that the person will wait more than 1 minutes is 
  4. Suppose that the person has already been waiting for 0.7 minutes. Find the probability that the person's total waiting time will be between 2.2 and 3.9 minutes 
  5. 90% of all customers wait at least how long for the train?  minutes.
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Expert Answer

Step 1

Note:

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Step 2
  1. Mean of the distribution:

Let X denotes the times from when a person arrives at the bus stop until the bus arrives. It follows uniform distribution from 0 to 7 minutes.

Here, a is 0 and b is 7.

The mean of the uniform distribution is obtained as 3.5, from the calculation given below:

ab
με
2
0 7
2
=3.5
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ab με 2 0 7 2 =3.5

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Step 3
  1. Standard deviation:

The standard deviation of uniform distribution is obtained as 0.7638...

2
(7-0)
12
= V0.5833
0.7638
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2 (7-0) 12 = V0.5833 0.7638

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