Question

Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. what is the probability that the time interval between two consecutive defective light bulbs will be at least 50 minutes?

Answer 1

In this case the time interval between two successive defective light bulbs is the Variable of interest.

Let X be a random variable which denotes the time interval in minutes between two successive defective bulbs.

We know that if X follows Uniform distribution in [a, b], then its probability density function is given by

It is given that time interval follows uniform distribution in interval 0 to 90. Therefore the probability density function is given by

We have to obatin the probability that the time interval between two consecutive defective light bulb is atleast 50 minutes. Then it is obtained by obtaining the probability for X>50, as X representing time interval. Then it is given by

Therefore, the probability is 0.444 that the time interval between two consecutive light bulbs is atleast 50 minutes.