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

Answer:

$Mean = 20$

$SD = 2.31$

Step-by-step explanation:

Given

$a = 16$

$b = 24$

Solving (a): The mean

The mean of a uniform distribution is:

$Mean = \frac{1}{2}(a + b)$

This gives:

$Mean = \frac{1}{2}(16 + 24)$

$Mean = \frac{1}{2}(40)$

$Mean = 20$

Solving (b): The standard deviation

The standard deviation is:

$SD = \sqrt{\frac{(b - a)^2}{12}}$

This gives:

$SD = \sqrt{\frac{(24 - 16)^2}{12}}$

$SD = \sqrt{\frac{(8)^2}{12}}$

$SD = \sqrt{\frac{64}{12}}$

$SD = \sqrt{5.333}$

$SD = 2.31$