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Discrete Probability Distributions Gateway 2000 Inc.

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Gateway 2000, Inc., receives large shipments of microprocessors from Intel Corp. It must try to ensure that the proportion of microprocessors that are defective is small. Suppose Gateway decides to test five microprocessors out of a shipment of thousands of them. Suppose that if at least one of the microprocessors is defective, the shipment is returned.
a. If Intel Corp.'s shipment contains 10% defective microprocessors, calculate the probability the entire shipment will be returned.
b. If Intel and Gateway agree that Intel will not provide more than 5% defective chips, calculate the probability that the entire shipment will be returned even though only 5% are defective.
c. Calculate the probability that the entire shipment will be kept by Gateway even though the shipment has 10% defective microprocessors

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The solution calculates the probabilities of the shipments being returned.

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Gateway 2000, Inc., receives large shipments of microprocessors from Intel Corp. It must try to ensure that the proportion of microprocessors that are defective is small. Suppose Gateway decides to test five microprocessors out of a shipment of thousands of them. Suppose that if at least one of the microprocessors is defective, the shipment is returned.
a. If Intel Corp.'s shipment contains 10% ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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