Suppose that SRMAP owns a computer manufacturing company and determines that 5 out of every 75 computers are defective. Determine the number of computers we would expect SRMAP to inspect until SRMAP finds its first defective. (a) 25(b) 30(c) 15(d) 50
Question
Suppose that SRMAP owns a computer manufacturing company and determines that 5 out of every 75 computers are defective. Determine the number of computers we would expect SRMAP to inspect until SRMAP finds its first defective. (a) 25(b) 30(c) 15(d) 50
Solution
The problem is asking for the expected number of trials until the first success. This is a geometric distribution problem. The formula for the expected value (mean) of a geometric distribution is 1/p, where p is the probability of success on each trial.
Step 1: Determine the probability of a computer being defective. The problem states that 5 out of every 75 computers are defective. So, the probability of a computer being defective is 5/75 = 1/15.
Step 2: Use the formula for the expected value of a geometric distribution. The expected number of computers SRMAP would need to inspect until it finds its first defective is 1/(1/15) = 15.
So, the answer is (c) 15.
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