Question

The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?

Answer 1

To calculate the probability that a randomly selected person is age 48 or older, we can use the z-score formula and a z-table or calculator. The probability is approximately 15.87%.

Step-by-step explanation:

To find the probability that the randomly selected person is age 48 or older, we need to calculate the area under the normal distribution curve to the right of 48. We can use the z-score formula:

z = (x - mean) / standard deviation

In this case, x = 48, mean = 41, and standard deviation = 7. By substituting these values into the formula, we can calculate the z-score and find the probability using a z-table or a calculator.

The z-score is found to be z = (48 - 41) / 7 = 1.

Using a z-table or calculator, we can find the probability that the z-score is less than 1, which is approximately 0.8413. Since we want the probability that the person is age 48 or older, we can subtract this probability from 1 to get 1 - 0.8413 = 0.1587, or approximately 15.87%.