Question

A manufacturing process produces semiconductor chips with a known failure rate of 5.3%. If a random sample of 275 chips are selected, approximately the probability that more than 13 will be defective. Use the normal approximation to the binomial with a correction for continua tee

Answer 1

SOLUTION:-

Given that:-

n = 275

p=0.053

1-p=0.947

Normal approximation to the binomial.

Mean = np = 275 x 0.053 = 14.575

sd = npq= Vnx px (1 – p)

sd = 14.575 x 0.947 = 3.66 = 3.72.

13 defective with continuity correction 13.5

Z-Value = ( 13.5 - 14.575 ) / 3.72 = -0.2889

Z-Value = -0.2889

Required probability =  0.386329 $\approx$ 0.39.