26 August, 18:18

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. 26 August, 19:48
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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