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

Answer:

d. 10 minutes and 1.33 minutes.

Step-by-step 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:

$M = \frac{a + b}{2}$

The variance of the uniform distribution is given by:

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

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

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

Mean:

$M = \frac{8 + 12}{2} = 10$

Variance:

$V = \frac{(12-8)^{2}}{12} = 1.33$

So the correct answer is:

d. 10 minutes and 1.33 minutes.