Question

suppose a production line stops for maintenance whenever a defective product is produced. if there is a 1% chance of a defective product, what is an upper bound on the probability that at least 175 products are made before a defect is discovered? (hint: find an upper bound, not the actual probability.

Answer 1

An upper bound on the probability that at least 175 products are made before a defect is discovered is 0.57 (Option C)

According to Markov's inequality, the chance that a positive real number is larger than or equal to a given positive random variable X is either less than or equal to the expected value of X divided by a.

Let X stand for the random variable that represents the first flaw found; X has a geometric distribution with p=0.01.

Then we'll have: E(X) = (1 - p) / p = (1 - 0.01) / 0.01 = 99

Markov's inequality has been used to create:

P(X ≥ 175) = E(X) / 175 = 99 / 175 = 0.5657 ≅ 0.57

Therefore, the highest limit on the likelihood that at least 175 goods be produced before a flaw is found is:

P(X ≥ 175) = 0.57

Therefore, option C is the correct choice.

To know more about Markov's inequality, refer to this link:

brainly.com/question/28902943

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COMPLETE QUESTION:

Suppose a production line stops maintenance whenever a defective product is produced. If there is a 1% chance of a defective product, what is an upper bound on the probability that at least 175 products are made before a defect is discovered? (Hint: Find an upper bound, NOT the actual probability.)

a. 0.34

b. 0.01

c. 0.57

d. 0.17