Question

A manufacturing process produces semiconductor chips with a known failure rate of 7.5%. If a random sample of 280 chips is selected, approximate the probability that at most 19 will be defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Answer 1

Answer)

N = 280

P = 0.075

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 21

N*(1-p) = 259

Both the conditions are met so we can use standard normal z table to estimate the probability

Z = (x - mean)/(s.d)

Given mean = n*p = 280*0.075 = 21

S.d = √{n*p*(1-p)} = 4.40738017420

P(x<=19)

By continuity correction

P(x<19.5)

Z = (19.5 - 21)/4.40738017420

Z = -0.34

From Z table, P(z<-0.34) = 0.3669