Question

The annual per capita consumption of bottled water was 33.7 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 33.7 and a standard deviation of 13 gallons.

What is the probability that someone consumed more than 34 gallons of bottled water?

Answer 1

To find the probability that someone consumed more than 34 gallons of bottled water, calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that someone consumed more than 34 gallons of bottled water, we need to calculate the area under the normal distribution curve to the right of 34 gallons. Step 1: Calculate the z-score using the formula: z = (x - mean) / standard deviation. Plugging in the values, we get z = (34 - 33.7) / 13 = 0.03. Step 2: Look up the z-score in the standard normal distribution table (or use a calculator) to find the corresponding cumulative probability. For z = 0.03, the cumulative probability is approximately 0.5129. Step 3: Subtract the cumulative probability from 1 to find the probability of consuming more than 34 gallons. 1 - 0.5129 = 0.4871, or 48.71%.