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Question by Max: Probability. Please help!?
An injection molding process leaves an average of 1.3 defects per bumper. Let Y and Z be the next two bumpers produced. Use an appropriate prob. function to evaluate:
a.)P[Y=2]
b.)P[Y>=1]
c.)sqr(Var Y)
d.)P[Y+Z>=2]

The problem does NOT say that it follows a normal distribution. This is quite literally all it gives. I’m assuming that this problem has something to do with the probability of 2 independent factors–I’ve looked at the section they are from but can’t find a thing. There are solutions if you have a standard deviation, but there wasn’t one given so I don’t know how to go about these. I have a normal distribution approx. table but I’m not sure if I can use it, or even how in this situation.

Best answer:

Answer by M3
the poisson distribution will be appropriate here. the formula is

P[x] = e^-m * m^x / x!

qa
m = 1.3, x = 2
P[2] = e^-1.3 * 1.3^2 /2!
= .2303
————

qb
P[>=1] = 1 – P[0] = 1 – e^-1.3 * 1.3^0 /0!
= .7275
———–

qc
variance of a posson distribution = m
sqrt(variance Y) = sqrt(1.3)
= 1,14
———

qd
for [Y+Z] , m = 2.6
applying the formula,
P[>=2] = 1 – { P[0] + P[1] }
= 1 – { e^-2.6 + e^-2.6*2.6/1! }
= .7326
———–

What do you think? Answer below!

Question by Max: Probability help?!?!?
An injection molding process leaves an average of 1.3 defects per bumper. Let Y and Z be the next two bumpers produced. Use an appropriate prob. function to evaluate:
a.)P[Y=2]
b.)P[Y>=1]
c.)sqr(Var Y)
d.)P[Y+Z>=2]

Best answer:

Answer by efqy
You’re presumably meant to assume a Poisson distribution with parameter 1.3

[The definition of Y and Z are wrong, and if your teacher/lecturer/textbook actually put that (“Let Y and Z be the next two bumpers produced”) they should be ashamed .

Y and Z should be “the number of defects on the next two bumpers produced, respectively”. If Y and Z were the bumpers themselves, they would not take values like 2, because bumpers are not numbers.]

a) just substitute 2 into the Poisson probability function with parameter 1.3

b) This is 1-P(Y=0)

c) what’s the variance of a Poisson random variable?

d) What’s the distribution of the sum of two independent Poissons?

Add your own answer in the comments!