Question

The random variable X has a uniform distribution with values between 16 and 24. What is the mean and standard deviation of X

Answer 1

`Mean = 20`

`SD = 2.31`

Explanation:

Given

`a = 16`

`b = 24`

Solving (a): The mean

The mean of a uniform distribution is:

`Mean = (1)/(2)(a + b)`

This gives:

`Mean = (1)/(2)(16 + 24)`

`Mean = (1)/(2)(40)`

`Mean = 20`

Solving (b): The standard deviation

The standard deviation is:

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

This gives:

`SD = \sqrt{((24 - 16)^2)/(12)}`

`SD = \sqrt{((8)^2)/(12)}`

`SD = \sqrt{(64)/(12)}`

`SD = √(5.333)`

`SD = 2.31`