Leaks occur in a pipeline at a mean rate of 1 leak per 1,000 meters. In a 2, 500

Question

Leaks occur in a pipeline at a mean rate of 1 leak per 1,000 meters. In a 2, 500-meter section of pipe, what is the probability of (a) no leaks? (b) Three or more leaks? c) sketch the probability distribution. (d) expected number of leaks? (e) Why not use the binomial? 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 next abnormal one is found? (b) What is the standard deviation? (c) Based on your answers to (a) and (b), why would it be difficult for a technician to maintain vigilance while inspecting pap smears?

Explanation / Answer

2 ) Given that Probability = 0.02 (2%)

so Expected value = Ex = number of success/ Probability

so for 1 success

Ex number of pam smears = 1/0.02 = 50

also , the variance is given as

Var = (1-p)/p^2 = (1-0.02)/ (0.02)^2= 2450

so standard deviation is sqrt(2450) = 49.5

c)

as the standard deviation is high 49.5 and mean is 50 , hence this means that abonormality can occur anywhere from 0 to 100 (rounded) , hence he must inspect each pap smear to maintain vigilance

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