Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.38. Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.7?

99.7% of the students have grade point averages that are between 1.42 and 3.7

Step-by-step explanation:

The Empirical Rule 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 of 2.56 and standard deviation of 0.38.

Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.7?

1.42 = 2.56 - 3*0.38

3.7 = 2.56 + 3*0.38

So both these scores are within 3 standard deviations of the mean, which means that 99.7% of the students have grade point averages that are between 1.42 and 3.7

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step-by-step explanation:

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