Question

What percentage of the population has a heart rate between 68 and 77

Answer 1

Answer:

49.87% of the population has a heart rate between 68 and 77.

Step-by-step explanation:

We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.

Let X = the data for the resting heart of adults

The z-score probability distribution for the normal distribution is given by;

                          Z  =  $\frac{X-\mu}{\sigma}$  ~ N(0,1)

where, $\mu$ = population mean = 68 beats per minute

           $\sigma$ = standard deviation = 3 beats per minute

Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)

    P(68 < X < 77) = P(X < 77) - P(X $\leq$ 68)

    P(X < 77) = P( $\frac{X-\mu}{\sigma}$ < $\frac{77-68}{3}$ ) = P(Z < 3) = 0.9987

    P(X $\leq$ 68) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{68-68}{3}$ ) = P(Z $\leq$ 0) = 0.50

The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.

Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%