Answer :
a. The relative frequency of rates less than 110 is approximately 95%.
b. The relative frequency of rates greater than 90 is approximately 32%.
c. The relative frequency of rates between 30 and 70 is approximately 68%.
What is Relative Frequency?
Relative frequency of a event is the measure of something happens relative to the total outcomes of that event.
The relative frequency can also be defined as, it is the ratio of subgroup frequency to the total frequency of any event.
a. To find the relative frequency of heart rates less than 110, we can use the 68-95-99.7 rule. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
The heart rate of 110 is 2 standard deviations above the mean (70 + 2 * 20 = 110). Therefore, we can infer that the relative frequency of rates less than 110 is approximately 95% based on the 68-95-99.7 rule.
b. Similarly, to find the relative frequency of heart rates greater than 90, we can use the 68-95-99.7 rule. The heart rate of 90 is 1 standard deviation above the mean (70 + 1 * 20 = 90). Since the 68-95-99.7 rule indicates that approximately 68% of the data falls within one standard deviation below and above the mean, we can infer that the relative frequency of rates greater than 90 is approximately 32%.
c. To find the relative frequency of heart rates between 30 and 70, we can again use the 68-95-99.7 rule. The heart rate of 30 is 2 standard deviations below the mean (70 - 2 * 20 = 30), and the heart rate of 70 is equal to the mean. Since the 68-95-99.7 rule indicates that approximately 68% of the data falls within one standard deviation below and above the mean, we can infer that the relative frequency of rates between 30 and 70 is approximately 68%.
Therefore:
a. The relative frequency of rates less than 110 is approximately 95%.
b. The relative frequency of rates greater than 90 is approximately 32%.
c. The relative frequency of rates between 30 and 70 is approximately 68%.
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