Take home Quiz chapter 14,15 NAME 1) Leakage from underground gasoline tanks at

Question

Take home Quiz chapter 14,15 NAME 1) 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 157 (b) What is the probability that 5 tanks leak? (c) What is the probability that less than 4 tanks leak? (d) What is the probability that 10 or more of the 15 tanks leak? (e) Now you do a larger study, examining a random sample of 1000 tanks nationally. What is the probability that at least 275 of these tanks are leaking? Use the normal approximation

Explanation / Answer

Answering all questions with calculations:

p(leak) = .25
n = 15

a. Mean = E(X) = np = .25*15 = 3.75

b. P(X=5) = 15C5(.25^5)(.75^10) = .1652

c. P(X<4) = P(X=0,1,2,3) = 15C0(.25^0)(.75^15)+..+15C3(.25^3)(.75^12) = 0.4613

d. P(X>=10) = P(X=10,11,12,13,14,15) = = 15C10(.25^10)(.75^5)..+= 15C15(.25^15)(.75^0) = 0.0008

e. Mean = np = .25*1000 = 250, Stdev = sqrt(npq) = sqrt(1000*.25*.75)=13.6931

We normalize using the params we have taken out above:

P(X>=275) = P(Z>= 275-250/13.6931) =1-.9661 = .0339

So, 3.39% or .339 chance of alteast 275 tanks are leaking

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