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30 July, 01:28

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?

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  1. 30 July, 03:39
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    99.996%

    Step-by-step 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%
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