10. Leakage from underground gasoline tanks at service stations can damage the e

Question

10. Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks leak. You examine 15 tanks chosen at random, independently of each other (a) What is the mean number of leaking tanks in such samples of 15? iple of (b) What is the probability that 10 or more of the 15 tanks leak? (c) Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 540 of these tanks are leaking? re

Explanation / Answer

n = 15 p = 0.25

(a) Mean = np = 15 * 0.25 = 3.75.

(b) X ~ Binom(15,0.25)

From the binomial tables, P(X >= 10) = 0.0008.

(c) X ~ Binom(2000, 0.25)

From the binomial tables, P(X >= 540) = 0.0213.

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