Question

In: Statistics and Probability

Four large batches of eggs are scheduled to be hatched in an incubator. Historical data suggests...

Four large batches of eggs are scheduled to be hatched in an incubator. Historical data suggests that the number of spoiled eggs (eggs that do not hatch) is Poisson distributed with mean 8 per batch.

a. what is the probability that there are at most 5 spoiled eggs in a batch?

B. find the probability that the total number of spoiled eggs in four batches is 20 of more?

Solutions

Expert Solution

(a)

Poisson Distribution with mean = 8 is given by:

for x =0, 1, 2,..

P(X5) = P(X = 0) + P(X= 1) + P(X=2) + P(X = 3) + P(X = 4) + P(X = 5)

So,

P(X5) = 0.19124

So,

Answer is:

0.19124

(b)

Poisson Distribution with mean = 8 X 4 = 32 is given by:

for x =0, 1, 2,..

P(X20) = 1 - P(X19)

By Table of Cumulative Probability Poisson Distribution, for Cumulative Probability for x = 19, we get P(X19) = 0.00934

So,

P(X20) = 1 - P(X19) = 1 - 0.00934 = 0.99066

So,

Answer is:

0.99066

orchestra answered 1 year ago

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