Assume the resting heart rates for a sample of individuals are normally distributed with a maan of 00 and a standard deviation of 20 . Use the 68.95 .997 rule to find the following quarticies a. The relative frequency of rates less than 120 using the $68.95-997$ rule is 0.975 ' (Round to three decimal places as needed) b. The relatwe frequency of rates greater than 100 using the $68.95-99.7$ rule is $\square$ (Round to three decimal places as needed)

Step 1 ：The problem is asking for the relative frequency of rates less than 120 and greater than 100 using the 68-95-99.7 rule. This rule is also known as the empirical rule, which states that for a normal distribution, almost all data falls within three standard deviations of the mean. Specifically, 68% falls within the first standard deviation, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 2 ：To solve this problem, we need to calculate the number of standard deviations away from the mean the values 120 and 100 are. Then, we can use the empirical rule to find the relative frequencies.

Step 3 ：For the first part of the question, we need to find the relative frequency of rates less than 120. This means we need to find the area under the curve to the left of 120.

Step 4 ：For the second part of the question, we need to find the relative frequency of rates greater than 100. This means we need to find the area under the curve to the right of 100.

Step 5 ：Let's start with the first part. The mean is 100 and the standard deviation is 20. The z-score for 120 is 1.0. Using the empirical rule, the relative frequency of rates less than 120 is approximately 0.841, or 84.1%. This means that about 84.1% of individuals have a resting heart rate less than 120.

Step 6 ：Now, let's move on to the second part of the question. The mean is 100 and the standard deviation is 20. The z-score for 100 is 0.0. Using the empirical rule, the relative frequency of rates greater than 100 is approximately 0.5, or 50%. This means that about 50% of individuals have a resting heart rate greater than 100.

Step 7 ：Final Answer: The relative frequency of rates less than 120 using the $68.95-99.7$ rule is approximately $0.841$ or $84.1\%$ and the relative frequency of rates greater than 100 using the $68.95-99.7$ rule is approximately $0.5$ or $50\%$. So, the answers are \(\boxed{0.841}\) and \(\boxed{0.5}\).