A large shipment of computer chips is known to contain 8% defective chips. Suppose you select 500 chips at random.
A. What distribution does the number of defective chips in the sample of 500 satisfy?
Distribution - Binomial
Number of trials n = 500
Probability of success (finding a defective chips) p = 8%
B. Suppose that you wish to calculate the probability that the number of defective chips in the sample is exactly 50. Write the exact formula for this number, but you are NOT required to evaluate the probability.
(b) Suppose that you wish to calculate the probability that the number of defective chips in the sample is exactly 50. Write the exact formula for this number, but you are NOT required to evaluate the probability.
P(X=x)= 200Cx *(0.08)^x*(1-0.08)^(200-x)
P(X=50) = 200C50 *(0.08)^50*(1-0.08)^(200-50)
C. What is the expected number of defective chips in your sample?
(c) What is the expected number of defective chips in your sample?
E(X) = n*p=200*0.08=16 chips
D. What is the standard deviation of the number of defective chips in the sample? (Please characterize its relevant parameters.)
(d) What is the standard deviation of the number of defective chips in the sample? use SD furumla in excell V(X)=n*p*(1-p)=200*0.08*(1-0.08)= 14.72 Standard deviation = Square root of V(X) = 14.72^0.5 = 3.837