Question

A​ four-year study of various brands of bottled water found that ​30% of bottled water is just tap water packaged in a bottle. Consider a sample of seven ​bottled-water brands, and let x equal the number of these brands that use tap water. Complete parts a through d.

Answer 1

To solve this question, we can use the concept of probability and the binomial distribution. Given that 30% of bottled water is tap water, we can calculate the probability that a specific number of brands use tap water using the binomial probability formula.

Step-by-step explanation:

In this question, we are asked to consider a sample of seven bottled water brands and determine the number of these brands that use tap water, denoted as x. We are given that 30% of bottled water is just tap water packaged in a bottle. To solve this problem, we can use the concept of probability.

Step-by-step explanation:

1. Since 30% of bottled water is tap water, the probability that one brand uses tap water is 0.30.
2. We are considering a sample of seven brands, so the number of brands that use tap water, x, follows a binomial distribution with n = 7 and p = 0.30.
3. To find the probability of a specific number of brands using tap water, we can use the binomial probability formula: P(x) = (n choose x) * p^x * (1-p)^(n-x).
4. In this case, we want to find the probability that x brands use tap water, so we substitute the values into the formula and calculate P(x).
5. For example, if we want to find the probability that exactly 3 brands use tap water, we would calculate P(3) = (7 choose 3) * 0.30^3 * (1-0.30)^(7-3).
6. You can repeat this calculation for different values of x to find the probabilities for the different possible outcomes.