The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a batch contains 1000 chips. Let the random variable X be the number of defective chips. a) Disregarding the number of chips, what probability distribution is the most appropriate to model the scenario? b) Why is the probability distribution valid to be approximated by a Normal probability distribution? What conditions are satisfied? c) What is the mean and variance of the random variable X? d) If we want to find the probability that X< 25, find the corresponding standard normal random variable Z. e) What is the probability that there are less than 25 chips in the lot?
The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a batch contains 1000 chips. Let the random variable X be the number of defective chips. a) Disregarding the number of chips, what probability distribution is the most appropriate to model the scenario? b) Why is the probability distribution valid to be approximated by a Normal probability distribution? What conditions are satisfied? c) What is the mean and variance of the random variable X? d) If we want to find the probability that X< 25, find the corresponding standard normal random variable Z. e) What is the probability that there are less than 25 chips in the lot?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:The manufacturing of semiconductor chips produces 2% defective chips.
Assume that the chips are independent and that a batch contains 1000 chips. Let the random
variable X be the number of defective chips.
a) Disregarding the number of chips, what probability distribution is the most appropriate
to model the scenario?
b) Why is the probability distribution valid to be approximated by a Normal probability
distribution? What conditions are satisfied?
c) What is the mean and variance of the random variable X?
d) If we want to find the probability that X < 25, find the corresponding standard normal
random variable Z.
е)
What is the probability that there are less than 25 chips in the lot?
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