Question

The assembly time for a product is uniformly distributed between 8 and 12 minutes.The mean and the variance of the assembly time are: a.4 minutes and 16 (minute)2 b.8 minutes and 12 (minute)2 c.12 minutes and 1.33 (minute)2 d.10 minutes and 1.33 (minute)2

Answer 1

d. 10 minutes and 1.33 minutes.

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 distribution is:

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

The variance of the uniform distribution is given by:

`V = ((b-a)^(2))/(12)`

The assembly time for a product is uniformly distributed between 8 and 12 minutes.

This means that
`a = 8, b = 12`.

Mean:

`M = (8 + 12)/(2) = 10`

Variance:

`V = ((12-8)^(2))/(12) = 1.33`

So the correct answer is:

d. 10 minutes and 1.33 minutes.