Question

2. Is the bottled water you’re drinking really purified water? A 4-year study of bottled water brands conducted by the Natural Resources Defense Council found that 25% of bottled water is just tap water packaged in a bottle. Consider a sample of five bottled water brands, and let Y equal the number of these brands that use tap water. A. What is the type of probability distribution for Y. B. Find P(Y=2) C. Find P(Y<1).

Answer 1

a.

The random variable has binomial distribution with parameters p = 0.25, n=5.

b.

`P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237`

Explanation:

a.

Remember what a random variable with binomial distribution is. It is a random variable that counts the number of successes and in n trials of an experiment.

In this case, if you have 0,1,2,3,4,5 bottles of water, your success is that the bottle has tap water, and the probability of that success is p = 0.25. and the number of trials is n = 5.

b.

Using the formula for the binomial distribution you get that

`P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237`