# Poisson and Binomial distribution clarification?

• Mar 6th 2011, 11:47 PM
ashvuck
Poisson and Binomial distribution clarification?
Home tub and shower stalls are made of composite materials in a production process that involves spraying resin, and moulding. Defects such as micro cracks (in spider web patterns) often appear in the final products. Although these defects do not affect the performance of the product, they are unappealing to customers. The number of defects per unit, Y, is a random variable that follows the Poisson distribution with mean
¸
=0.8.

(a)
Sketch the probability distribution for Y.

(b)
Find the probability that a tub and shower unit will have between two and four (inclusive) defects.

(c)
Find the probability that a production run of 120 units will have more than 45 defect-
free units. [Give an exact solution, an approximate solution, or just write down theexpression that needs to be evaluated to get the answer, if your calculator does not have the memory to evaluate it.]

Ok this is a tute question from class i got the first two answers, but i dont get how to do the last question, my teacher mention something about using bionomial distribution instead but how does that work if it follows a poisson distribution pattern???

• Mar 7th 2011, 01:42 AM
mr fantastic
Quote:

Originally Posted by ashvuck
Home tub and shower stalls are made of composite materials in a production process that involves spraying resin, and moulding. Defects such as micro cracks (in spider web patterns) often appear in the final products. Although these defects do not affect the performance of the product, they are unappealing to customers. The number of defects per unit, Y, is a random variable that follows the Poisson distribution with mean

¸
=0.8.
(a)

Sketch the probability distribution for Y.

(b)

Find the probability that a tub and shower unit will have between two and four (inclusive) defects.

(c)

Find the probability that a production run of 120 units will have more than 45 defect-
free units. [Give an exact solution, an approximate solution, or just write down theexpression that needs to be evaluated to get the answer, if your calculator does not have the memory to evaluate it.]

Ok this is a tute question from class i got the first two answers, but i dont get how to do the last question, my teacher mention something about using bionomial distribution instead but how does that work if it follows a poisson distribution pattern???

Let X be the random variable 'number of units with no defect'. Then X ~ Binomial(p, n = 120) where p = Pr(Y = 0).

• Mar 7th 2011, 06:16 AM
ashvuck
What is the probability of success, the p value? is it 0.8?
• Mar 7th 2011, 10:41 AM
mr fantastic
Quote:

Originally Posted by ashvuck
What is the probability of success, the p value? is it 0.8?

I told you what p was:

Quote:

p = Pr(Y = 0).
You're expected to know what Y is and how to do this basic calculation.