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?

Answer 1

99.996%

Explanation:

Given:-

Distribution of the number of steps he takes is normally distributed with a mean u = 10,000 and a standard deviation s = 1,500 steps.

Find:-

One day he took 15,000 steps. What was his percentile on that day?

Solution:-

- We will denote a random variable X the number of steps taken by the student to follows normal distribution:

X ~ N ( 10,000 , 1500^2 )

- We will standardize the value of 15,000 steps and find the Z-score:

Z = ( X - u ) / s

Z = (15,000 - 10,000) / 1500

Z = 3.333

- The probability of Z less than the standardized value denotes the percentile value:

percentile = P ( Z < 3.333 ) = 99.996%