Question

The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixtures or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes

Answer 1

The numbers of doors that will have no blemishes will be about 6065 doors

Explanation:

Let the number of counts by the worker of each blemishes on the door be (X)

The distribution of blemishes followed the Poisson distribution with parameter
`\lambda =0.5` / door

The probability mass function on of a poisson distribution Is:

`P(X=x) = (e^(- \lambda ) \lambda ^x)/(x!)`

`P(X=x) = (e^(- \ 0.5 )( 0.5)^ x)/(x!)`

The probability that no blemishes occur is :

`P(X=0) = (e^(- \ 0.5 )( 0.5)^ 0)/(0!)`

`P(X=0) = 0.60653`

P(X=0) = 0.6065

Assume the number of paints on the door by q = 10000

Hence; the number of doors that have no blemishes is = qp

=10,000(0.6065)

= 6065