A manufacturing process produces semiconductor chips with a known failure rate of 6.3%. Assume that chip failures are independent of one another. You will be producing 2,000 chips tomorrow.
a. What is the name of the probability distribution of the number of defective chips produced tomorrow?
b. Find the expected number of defective chips produced.
c. Find the standard deviation of the number of defective chips.
d. Find the (approximate) probability that you will produce fewer than 130 defects.
e. Find the (approximate) probability that you will produce more than 120 defects.
f. You just learned that you will need to ship 1,860 working chips out of tomorrow’s production of 2,000. What are the chances that you will succeed? Will you need to increase the scheduled number produced?
g. If you schedule 2,100 chips for production, what is the probability that you will be able to ship 1,860 working ones?