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# Answer: Suppose that X has a Poisson distribution with a ISBN: 9781118539712 55

## Solution for problem 97E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 97E

Suppose that X has a Poisson distribution with a mean of 64. Approximate the following probabilities: Step-by-Step Solution:

Step 1 of 3:

Let X has a poisson distribution with a mean of 64.

We have to find the following probabilities.

P(X>72)P(X<64)P(60<X 68)

Step 2 of 3:

Here X~Poisson( =64).

Mean, =64.

Variance, =64.

Let Z follows approximate normal distribution and variable, Z= .

P(X>72)= P(Z> )    [ by adding the correction factor 0.5]

= P(Z>1.06)

= 1- P(Z<1.06)

From the standard normal table, P(Z<1)= 0.8554.

P(X>72)= 1- 0.8554

= 0.1446

Therefore, the probability P(X>72) is 0.1446.

(b)

P(X<64)= P(Z< )  [ by subtracting the correction factor 0.5]

= P(Z< )

= P(Z<-0.062)

From the standard normal table, P(Z<0.062)= 0.4761.

Therefore, the probability P(Z<64)= 0.4761

Step 3 of 3

##### ISBN: 9781118539712

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