A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution?
A)7,533
B)8,078
C)10,000
D)12,467

Question

Quizplus · Accepted Answer

To find the number of steps he would have to take to make the top 5%, we need to find the z-score which corresponds to the 95th percentile. Using a calculator or a z-table, we find that the z-score for the 95th percentile is approximately 1.645. We can use the formula z = (x - μ) / σ, where z is the z-score, x is the number of steps he takes, μ is the mean of 10,000, and σ is the standard deviation of 1,500. Rearranging this formula, we get x = z*σ + μ = 1.645 * 1500 + 10000 = 12,467. Therefore, he would have to take 12,467 steps to make the top 5%.

A Health Conscious Student Faithfully Wears a Device That Tracks