Question

the average resting heart rate of a population is 87 beats per minute, with a standard deviation of 11.5 bpm. find the z - scores that correspond to each of the following heart rates. round your answers to the nearest hundredth, if necessary.
(a) 98 bpm
z =
(b) 68 bpm
z =

Explanation:

Part (a)

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the population mean, and $\sigma$ is the population standard deviation. Here, $\mu = 87$, $\sigma=11.5$, and $x = 98$.

Step2: Substitute values into formula

Substitute $x = 98$, $\mu=87$, and $\sigma = 11.5$ into the formula: $z=\frac{98 - 87}{11.5}=\frac{11}{11.5}\approx0.96$ (rounded to the nearest hundredth).

Part (b)

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the population mean, and $\sigma$ is the population standard deviation. Here, $\mu = 87$, $\sigma = 11.5$, and $x=68$.

Step2: Substitute values into formula

Substitute $x = 68$, $\mu = 87$, and $\sigma=11.5$ into the formula: $z=\frac{68 - 87}{11.5}=\frac{- 19}{11.5}\approx - 1.65$ (rounded to the nearest hundredth).

Answer:

(a) $z\approx0.96$

(b) $z\approx - 1.65$