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. One day he took 15,000 steps. What was his percentile on that day?
A)95%
B)97.7%
C)99.7%
D)100%

Question

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. One day he took 15,000 steps. What was his percentile on that day? ​​
A)95%
B)97.7%
C)99.7%
D)100%

Quizplus · Accepted Answer

To find the percentile, we calculate the z-score: z = (X - μ) / σ = (15000 - 10000) / 1500 = 3. A z-score of 3 corresponds to the 99.7th percentile in a standard normal distribution.

A Health Conscious Student Faithfully Wears a Device That Tracks