Answer to Question #348126 in Statistics and Probability for Dan

Question

A quality control engineer knows that a flash drive produced by a company pass the company’s standard 95% of the time. He usually does a random checking of 20 flash drives from the day’s production and approves the whole production when no more than flash drives fail to meet the standards. What is the probability that the quality control engineer accepts the whole production for the day?

Answer 1

Let $X=$ the number of the defective flash drives: $X\sim Bin(n, p).$

Given $n=20,q=0.95, p=1-q=0.05$

$$P(X\le1)=P(X=0)+P(X=1)$$

$$=\dbinom{20}{0}(0.05)^{0}(0.95)^{20-0}+\dbinom{20}{1}(0.05)^{1}(0.95)^{20-1}$$

$$=0.735839524944$$