Question

A manufacturing process produces semiconductor chips with a known failure rate of 6.9%. If a random sample of 300 chips is selected, approximate the probability that fewer than 17  will be defective. Use the normal approximation to the binomial with a correction for continuity. (at least 3 decimal places)

Answer 1

Solution :

Given that,

p = 6.9%=0.069

q = 1 - p =1-0.069=0.931

n = 300

Using binomial distribution,

Mean = = n * p = 300*0.069=20.7

Standard deviation = = n * p * q =   300*0.069*0.931=4.39

Using continuity correction ,

P(x< 17 ) = P((x - ) / < (16.5-20.7) /4.39 )

= P(z < -0.96)

Using z table

Probability = 0.1685