Question

In the inspection of tin plate produced by a continuous electrolytic process, 0.2 imperfection is spotted per minute on average. Find the probabilities of spotting.

(a) one imperfection in 3 minutes.

(b) at least two imperfections in 5 minutes.

Answer 1

Solution:

Given: In the inspection of tin plate produced by a continuous electrolytic process, 0.2 imperfection is spotted per minute on average.

Thus X = Number of imperfection is spotted per minute follows a Poisson distribution with parameter

Part a) P(  spotting one imperfection in 3 minutes) =..............?

That is: P( X = 1) = ............?

We are given 0.2 imperfection is spotted per minute on average. , but we have to find probability of  spotting one imperfection in 3 minutes, so we need to find new parameter per 3 minutes.

For one minute we have , then for 3 minutes we get:  

Thus using probability mass function of Poisson distribution we get:

Use excel or scientific calculator to find : e^-0.6

Excel command:

=EXP(-0.6)

=0.548812

Thus probability of  spotting one imperfection in 3 minutes is 0.3293

Part b) P( Spotting  at least two imperfections in 5 minutes) =...........?

For one minute

we have , then for 5 minutes we get:  

Thus using probability mass function of Poisson distribution we get:

Thus probability of  spotting at least two imperfections in 5 minutes is 0.2642.