Question 7: (Text 5.88) The potential buyer of a particular engine requires (amo

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Question 7: (Text 5.88) The potential buyer of a particular engine requires (among other things) that the engine start successfully 10 times in succession. Suppose that the probability of a successful start is 0.99 and that the outcomes of attempted starts are independent. a) What is the probability that the engine is accepted after 10 starts. (i.e. the engine starts on every attempt of the first 10 attempts.) b) What is the probability that 12 attempts are needed before 10 successive successful starts occurs? Question 8: (Text 5.94) A production process produces electronic component parts. It is presumed that the probability of a defective part is 0.01. During a test of this presumption, 500 parts are sampled randomly a) 15 defectives are observed in the sample. What is your response to the presumption that the process has 1% defectives? (Provide a probabilistic assessment of the situation). b) Under the presumption of a process that generates 1% defective components, what is the probability that only 3 parts will be found defective in the sample? c) Repeat parts a) and b) using the Poisson approximation to the Binomial.

Explanation / Answer

7. a. There are two outcomes-success (engine starts successfully) and failure (engine doesnot start successfully), and probability of success, p=0.99. There are n=10 random, independent trials, and probability of success i sconstant throughout the trials. Use Binomial distribution to calculate the probabilities. Assume X denote number of successful starts.

P(X=10)=10C10(0.99)^10(1-0.99)^0=0.9044

b. P(X=10)=12C10(0.99)^10(1-0.99)^2=0.0060

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