Question

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

Answer 1

Answer:

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

Step-by-step 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%.