Question

Suppose the amount of time to finish assembling a component is exponentially distributed with an average of 2 minutes.

(a) What is the probability that it takes more than 5 minutes to assemble a component? (b) If 100 components are randomly selected, what is the probability that the average amount of time to assemble these100 components is more than 2.3 minutes?

Answer 1

Average time to finish assembling a component, = 2 min

Thus, mean number of components assembled in a minute, = 0.5

Standard deviation of time required to assemble a component

= = 2 min

(a) Let x denote the time required (in minutes) to assemble a component

P(x > 5) = 1 - P(x ≤ 5)

= 1 - F(5) =

= = 0.082

(b) From Central limit theorem, the sampling distribution of the average amount of time to assemble 100 components can be approximated to Normal distribution

where sample mean = = 2 min

and standard deviation = = = 0.2

Let denote the average amount of time to assemble 100 components

To find P( > 2.3)

The Corresponding z score = (2.3 - 2)/0.2 = 1.5

Thus, required probability = P(Z > 1.5) = 0.0668