Question

if its known that the probability of an item by a certain machine will be defective is 0.05, if the product item are sent to the market in packets of 20 find no. of packet containing at least, exactly and at most 2 defective item in a consignment of 1000 packets​

Answer 1

Step-by-step explanation:

ANSWER

By using Poisson distribution,

P(x;μ)=

x!

e

−μ

μ

x

μ: The mean number of successes that occur in a specified region(parameter)

x: The actual number of successes that occur in a specified region.

P(x;μ): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is μ

Here, μ = 100×0.01=1

P(x;μ)=P(x=0;1)+P(x=1;1)

P(x;1)=

0!

e

−1

1

0

+

1!

e

−1

1

1

=e

−1

+e

−1

=2e

−1

=

e

2