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22 March, 21:29

The time to complete an exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68-95-99.7 rule, what percentage of students will complete the exam in less than 60 minutes

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  1. 22 March, 21:32
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    16% of students will complete the exam in less than 60 minutes

    Step-by-step explanation:

    The Empirical Rule (68-95-99.7) states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean = 70

    Standard deviation = 10

    What percentage of students will complete the exam in less than 60 minutes

    60 = 70-10

    So 60 is one standard deviation below the mean

    By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean, that is, from 60 to 80 minutes. The other 100-68 = 32% is outside this interval. Since the normal distribution is symmetric, 16% of those are below 60 and 16% of those are above 80.

    16% of students will complete the exam in less than 60 minutes
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