Question

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.

- 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.

Step 1

**Note:**

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Step 2

**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:

Step 3

**Standard deviation:**

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

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