Question

scores on the gre (graduate record examination) are normally distributed with a mean of 551 and a standard deviation of 109. use the 68 - 95 - 99.7 rule to find the percentage of people taking the test who score between 224 and 878. the percentage of people taking the test who score between 224 and 878 is %

Explanation:

Step1: Calculate the number of standard deviations from the mean

Let \(\mu = 551\) (mean) and \(\sigma=109\) (standard deviation).
For \(x = 224\), \(z=\frac{x-\mu}{\sigma}=\frac{224 - 551}{109}=\frac{- 327}{109}=-3\)
For \(x = 878\), \(z=\frac{x-\mu}{\sigma}=\frac{878 - 551}{109}=\frac{327}{109}=3\)

Step2: Apply the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule states that for a normal distribution:

• Approximately \(68\%\) of the data lies within \(z=-1\) and \(z = 1\)
• Approximately \(95\%\) of the data lies within \(z=-2\) and \(z = 2\)
• Approximately \(99.7\%\) of the data lies within \(z=-3\) and \(z = 3\)

Answer:

\(99.7\)