Question

The time required to assemble a part follows an exponential probability distribution with a mean of 5 minutes. What is the probability that the part can be assembled between 3 and 5 minutes? what is the probability that exactly three parts can be assembled in 10 minutes?

Answer 1

(a)

Probability Density Function of Exponential Distribution with mean = 5 is given by:

                 for x 0

So,

between the limits 3 to 5

Applying limits, we get:

So,

Answer is:

0.1809

(b)

Probability that one part can be assembled in 10 minutes is given by:

between limits 0 to 10.

Applying limits, we get:

Probability that one part can be assembled in 10 minutes =

So,

Probability that three parts can be assembled in 10 minutes = p³ = 0.8647³ = 0.6465

So,

Answer is:

0.6465