Identifying Unusual Values with the Range Rule of Thumb. In Exercises 33–36, use the range rule of thumb to determine whether a value is unusual.

Pulse Rates of Males Based on Data Set 1 in Appendix B, males have pulse rates with a mean of 67.3 beats per minute and a standard deviation of 10.3 beats per minute. Is it unusual for a male to have a pulse rate of 45 beats per minute? (All of these pulse rates are measured at rest.) Explain.

Answer :

Step 1 of 1 :

Given Pulse Rates of Males Based on Data Set 1 in Appendix B, males have pulse rates with a mean of 67.3 beats per minute and a standard deviation of 10.3 beats per minute.

We know that mean μ = 67.3 and standard deviation σ = 10.3

According to the range rule of thumb, most values should lie within 2 standard deviations of the mean.

We can therefore identify “unusual” values by determining if they lie outside these limits:

Maximum usual value = μ + 2σ

Maximum usual value = 67.3 + 2(10.3)

Maximum usual value = 67.3 +20.6

Maximum usual value = 87.9

Minimum usual value = μ – 2σ

Minimum usual value = 67.3 + 2(10.3)

Minimum usual value = 67.3 -20.6

Minimum usual value = 46.7

Unusual for a male to have a pulse rate of 45 beats per minute.

We know that Minimum usual value = 46.7

So 45 < 46.7

Yes.It is unusual for a male to have a pulse rate of 45 beats per minute.

The pulse rate of 45 beats per minute is not between the minimum usual value of 46.7 beats per minutes and the maximum usual value of 87.9 beats per minute.