Question

The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 2 to 7. Find the mean and standard deviation of this random variable. (Round your answers to 2 decimal places.) Mean Standard deviation

Answer 1

The mean is 4.5 and the standard deviation is 1.44.

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

`M = ((a + b))/(2)`

The standard deviation of the uniform probability distribution is:

`S = \sqrt{((b-a)^(2))/(12)}`

Uniformly distributed random variable ranging from 2 to 7.

This means that
`a = 2, b = 7`.

So

`M = ((2 + 7))/(2) = 4.5`

`S = \sqrt{((b-a)^(2))/(12)} = \sqrt{((7 - 2)^(2))/(12)} = 1.44`

The mean is 4.5 and the standard deviation is 1.44.