Question

A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5. According to the Empirical Rule (68-95-99.7% Rule), approximately what percent of the values will be between 75 and 85

Answer 1

According to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

What is empirical rule?

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%$

Here, we had  where mean of distribution of X is $\mu$ and standard deviation from mean of distribution of X is $\sigma$.

A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5.

$\mu=80\\\sigma=5$

The percentage for the interval of values between 75 and 85 has to be found out. From the 68%, the interval is,

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(80 - 5 < X < 80+ 5) = 68\%\\P(75 < X < 85) = 68\%$

Thus, according to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

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