68-95-99.7 rule

Assume the resting pulse rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 15. Use the 68-95-99.7 rule to find the following quantities.
a. Percentage of pulse rates less than 70
b. Percentage of pulse rates between 55 and 70
c. Percentage pulse of rates between 70 and 100.

Correct answer:

a =  49.85 %
b =  34 %
c =  47.5 %

Step-by-step explanation:

$$\begin{gathered} m=70 \\ \sigma =15 \\ a=99.7/2=49.85\% \end{gathered}$$

$$\begin{gathered} s_1=m-\sigma =70-15=55 \\ b=68/2=34\% \end{gathered}$$

$$\begin{gathered} s_2=m+2\cdot \sigma =70+2\cdot 15=100 \\ c=95/2=47.5\% \end{gathered}$$

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