Question

A plant has three assembly lines that produce memory chips. Line 1 produces 50% of the chips and has defective rate of 4%, line 2 produces 30% of the chips and has a defective rate of 5%, line 3 produces 20% of the chips and has a defective rate of 1%.

A chip is randomly selected. Find the probability that the chip is defective. Given that the chip is defective, find the probability that the chips is produced on line 1.Every day a random sample of 100 chips is drawn and every chip is tested. Let the random variable X be the number of defective chips in the sample.

Find the probability, that in the random sample are exactly 5 defective chips.

Determine the exptected value and the variance of X.

Find an upper bound for the number of defective chips in the sample, so that the number of defective chips is less or equal this upper bound for 95% of all samples.

Ich bedanke mich für jede Hilfe.

Answer 1

a) 0.5*0,04+0,3*0,05+0,2*0,01

b) 0,5*0,04/(0.5*0,04+0,3*0,05+0,2*0,01)

c) p= 0.5*0,04+0,3*0,05+0,2*0,01

-> (100über5)*p^5*(1-p)^95