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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.42. Using the empirical rule, what percentage of the students have grade point averages that are less than 2.96? Please do not round your answer.

Respuesta :

Using the Empirical Rule, it is found that 84% of the students have grade point averages that are less than 2.96.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, 2.96 is one standard deviation above the mean. We have that:

  • The normal distribution is symmetric.
  • Of the 50% of the measures below the mean, all are below 2.96.
  • Of the 50% of the measures above the mean, 68% are below 2.96.

Hence the percentage is given by:

P = 50% + 0.68 x 50% = 50% + 34% = 84%.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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