A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the days does he exceed 13,000 steps?
A)2.28%
B)5%
C)95%
D)97.72%

Question

Quizplus · Accepted Answer

To find the percentage of days he exceeds 13,000 steps, we calculate the z-score: z = (13,000 - 10,000) / 1,500 = 2. Using the standard normal distribution table, the probability of a z-score less than 2 is 97.72%. Therefore, the probability of exceeding 13,000 steps is 100% - 97.72% = 2.28%.

A Health Conscious Student Faithfully Wears a Device That Tracks