77.4k views
5 votes
Scores on the GRE​ (Graduate Record​ Examination) are normally distributed with a mean of 573 and a standard deviation of 84. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 489 and 573

The percentage of people taking the test who score between 489 and 573 is

1 Answer

6 votes

Answer:

The percentage of people taking the test who score between 489 and 573 is 34%.

Explanation:

The Empirical Rule 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, we have that:

Mean of 573, standard deviation of 84

Percentage of people taking the test who score between 489 and 573

The mean is 573.

489 = 573 - 84, which means that 489 is one standard deviation below the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are below the mean.

So between one standard deviation below the mean and the mean, the percentage is 68/2 = 34%

The percentage of people taking the test who score between 489 and 573 is 34%.

User Loghorn
by
4.6k points