Question

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

Answer 1

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

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 =
`(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(
`(X-\mu)/(\sigma)` <
`(77-68)/(3)` ) = P(Z < 3) = 0.9987

P(X
`\leq` 68) = P(
`(X-\mu)/(\sigma)`
`\leq`
`(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%