Question

In: Statistics and Probability

If P=0.4% and n =600. Is the poison distribution a reasonable approximation distribution of the binomial...

If P=0.4% and n =600. Is the poison distribution a reasonable approximation distribution of the binomial distribution?

Yes or No

What is the mean of this binomial distribution ( and the mean of poison distribution used to approximate it)

Mean=

What is the actual mean of this binomial distribution

Standard deviation (actual)=

What is the mean of the approximate poison distribution?

Standard deviation approximate

Are these values in reasonable agreement

Solutions

Expert Solution

(1)

Question:

If P=0.4% and n =600. Is the poison distribution a reasonable approximation distribution of the binomial distribution?

Correct opton:
Yes

Explanation:

n = 600

p = 0.004

So,

Conditions are:

(i) n = 600 > 20

(ii) np = 600 X 0.004 = 2.4 < 5

So,

both conditions are satisfied.

(2)

Question:

What is the mean of this binomial distribution ( and the mean of poison distribution used to approximate it)

Mean = 600 X 0.004 = 2.4

(3)Question:

What is the actual mean of this binomial distribution

Mean = 600 X 0.004 = 2.4

(4)

Question:

Standard deviation (actual)=

So,

Standard deviation (actual)= 1.5461

(5)

Question:

What is the mean of the approximate Poisson distribution?

Mean of the approximate poison distribution = = 2.4

(6)

Question:

Standard deviation approximate

Standard deviation approximate of the approximate poison distribution =

So,

Standard deviation approximate = 1.5492

(7)

Question:

Are these values in reasonable agreement ?

Yes

because Standard deviation (binomial)= 1.5461 is close to Standard deviation approximate of the approximate poison distribution = 1.5492

orchestra answered 1 year ago

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