The question you've uploaded pertains to applying the empirical rule to a normal distribution. Let's break it down:

The Empirical Rule (also known as the 68-95-99.7 rule) states:

• 68% of data lies within one standard deviation of the mean.
• 95% lies within two standard deviations.
• 99.7% lies within three standard deviations.

In this case, we are given:

• Mean = 59
• Standard deviation = 8
• We're asked to find the percentage of data between 59 and 83.

First, let’s find the number of standard deviations from the mean to the two values:

• 59 is the mean, so it's 0 standard deviations away.
• 83 is $83 - 59 = 24$ units above the mean.

To find how many standard deviations this is, divide by the standard deviation: $\frac{24}{8} = 3$

So, the value 83 is 3 standard deviations above the mean. According to the empirical rule, this means we are looking at data between the mean (59) and 3 standard deviations above the mean (83). This range falls under the 68% + 95% area, which is the 68% in the first standard deviation, plus the 95% within the first two standard deviations.

To find the percentage between 59 and 83, this is simply the first 68% and 95% together (68% covers up to one standard deviation, and 95% includes up to two standard deviations). Therefore, between 59 and 83, the area covered is about 68%.

So, the answer is approximately 68%.

Let me know if you need more details or have any other questions!

Here are 5 related questions you might find interesting:

1. How would the percentage change if the value were 87 (another value higher than 83)?
2. What is the percentage of data between 51 and 67, where these values are 1 standard deviation below and above the mean?
3. How can the empirical rule be applied to a data set that is not perfectly normal?
4. What is the 95% range of this distribution?
5. What are the key differences between the empirical rule and Chebyshev's inequality?

Tip: The empirical rule works best with a bell-shaped distribution (normal distribution). Always check that your data appears to follow this shape before applying it!