Question

Suppose that the number of Chipotle burritos consumed per year by U.S. teens is normally distributed with a mean of 10 and a standard deviation of 5 . What percentage of U.S. teens consume between 5 and 20 burritos per year?

Answer 1

To find the percentage of U.S. teens consuming between 5 and 20 burritos per year, we need to calculate the z-scores for both values and find the corresponding area under the normal distribution curve. Using the z-scores, we can find the percentage of teens consuming less than 5 burritos and more than 20 burritos, subtract them from 100%, and get the percentage between 5 and 20 burritos.

Step-by-step explanation:

To find the percentage of U.S. teens consuming between 5 and 20 burritos per year, we need to calculate the z-scores for both values and find the corresponding area under the normal distribution curve.

To calculate the z-score for 5 burritos, we use the formula: z = (x - mean) / standard deviation. Substituting the given values, we get z = (5 - 10) / 5 = -1.

Similarly, for 20 burritos, the z-score is z = (20 - 10) / 5 = 2.

Using a standard normal distribution table or calculator, we can find the area to the left of -1 and 2, which represents the percentage of teens consuming less than 5 and more than 20 burritos respectively. The percentage between 5 and 20 burritos can be found by subtracting these two percentages from 100%.

Therefore, the percentage of U.S. teens consuming between 5 and 20 burritos per year is approximately 81.85%.