Question

Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of 40 components can be viewed as the 40 trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 5%. Suppose a random sample of five items from a recent shipment is tested. Assume that 5% of the shipment is defective and this probability do not change from trial to trial (follows a binomial distribution). What is the probability that one item in the sample are defective. (Use four decimal accuracy for your intermediate and final answer calculations) Question 1 options: 0.4705 0.3856 0.5646 0.2706

(please show in excel)

Answer 1

Binomial probability is given by  

P(X=x) = C(n,x)*px*(1-p)(n-x)

where  
Sample size , n =    40
Probability of an event of interest, p =   0.05

P ( X =    1   ) = C(   40   ,   1   )*   0.05   ^   1   *   0.950   ^   39   = 0.2706(answer)

excel formula:   =BINOM.DIST(1 ,40, 0.05, FALSE)

answer: = 0.2706