Question

the average resting heart rate of a population is 88 beats per minute, with a standard deviation of 12 bpm. find the z-scores that correspond to each of the following heart rates. round your answers to the nearest hundredth, if necessary. (a) 101 bpm z = (b) 75 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, $\mu = 88$, $\sigma=12$, and $x = 101$.

Step2: Substitute values into formula

Substitute $x = 101$, $\mu=88$, and $\sigma = 12$ into the formula: $z=\frac{101 - 88}{12}=\frac{13}{12}\approx1.08$ (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, $\mu = 88$, $\sigma = 12$, and $x=75$.

Step2: Substitute values into formula

Substitute $x = 75$, $\mu = 88$, and $\sigma=12$ into the formula: $z=\frac{75 - 88}{12}=\frac{- 13}{12}\approx - 1.08$ (rounded to the nearest hundredth).

Answer:

(a) $z\approx1.08$
(b) $z\approx - 1.08$