At a certain clinic, 2 percent of all pap smears show signs of abnormality. (a) What is the expected number of pap smears that must be inspected before the first abnormal one is found? Expected number of pap smears

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Mathematics

Ice Queen

1 April, 13:49

At a certain clinic, 2 percent of all pap smears show signs of abnormality. (a) What is the expected number of pap smears that must be inspected before the first abnormal one is found? Expected number of pap smears

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Matilda Obrien · Answer 1

The expected amount of pap smears that must be inspected before the first abnormal one is found is 50

Step-by-step explanation:

If 2 percent of all pap smears show signs of abnormality, then the probability that a pap smear is abnormal is 0.02.

Let X be the amount of pap smears needed before the first abnormal case is found. X has geometric ditribution with parameter p = 0.02. The mean of X, in other words, the expected amount of cases that must be inspected before the first abnormal one appears, is 1/p = 1/0.02 = 50.