Question

A manufacturing process produces semiconductor chips with a known failure rate of

7.5%

If a random sample of

275

chips is selected, approximate the probability that more than

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

Solution :

Given that,

p = 0.075

q = 1 - p =1-0.075=0.925

n = 275

Using binomial distribution,

= n * p = 275*0.075=20.625

= n * p * q = 275*0.075*0.925=4.3679

Using continuity correction

,P(x >19 ) = 1 - P(x < 19.5)

= 1 - P((x - ) / < (19-20.625) / 4.3679)

= 1 - P(z < -0.37)   

Using z table   

= 1-0.3557

=0.6443

probability= 0.644