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Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. Using the 68-95-99.7 rule, what percentage of students score above 86?

Answer :

Approximately 32% of students scored above 86 on the university exam.

To determine the percentage of students who score above 86, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule, in a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 78 and the standard deviation is 8, we can calculate the z-score for 86 using the formula:

z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (86 - 78) / 8 = 1

Since 86 is one standard deviation above the mean, we know that approximately 68% of students scored below 86. Therefore, the percentage of students who score above 86 can be estimated as 100% - 68% = 32%.

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