Question

the average resting heart rate of a population is 87 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) 96 bpm z = (b) 70 bpm z = question 8 the average height of american adult males is 177 cm, with a standard deviation of 7.4 cm. meanwhile, the average height of indian males is 165 cm, with a standard deviation of 6.7 cm. which is taller relative to his nationality, a 173 - cm american man or a 153 - cm indian man? the american man the indian man

Explanation:

Part (a) and (b) (Heart Rate z - scores)

The formula for calculating 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, \(\mu = 87\) bpm and \(\sigma=12\) bpm.

Step 1: Calculate z - score for \(x = 96\) bpm

Substitute \(x = 96\), \(\mu=87\) and \(\sigma = 12\) into the z - score formula.
\(z=\frac{96 - 87}{12}=\frac{9}{12}=0.75\)

Step 2: Calculate z - score for \(x = 70\) bpm

Substitute \(x = 70\), \(\mu = 87\) and \(\sigma=12\) into the z - score formula.
\(z=\frac{70 - 87}{12}=\frac{- 17}{12}\approx - 1.42\)

Part (Question 8: Height Comparison)

We need to calculate the z - scores for the heights of the American man and the Indian man and then compare them. The z - score formula is \(z=\frac{x-\mu}{\sigma}\)

Step 1: Calculate z - score for the American man

For the American man, \(x = 173\) cm, \(\mu=177\) cm, \(\sigma = 7.4\) cm.
\(z_{American}=\frac{173 - 177}{7.4}=\frac{-4}{7.4}\approx - 0.54\)

Step 2: Calculate z - score for the Indian man

For the Indian man, \(x = 153\) cm, \(\mu = 165\) cm, \(\sigma=6.7\) cm.
\(z_{Indian}=\frac{153 - 165}{6.7}=\frac{-12}{6.7}\approx - 1.79\)

Since \(- 0.54>-1.79\), the American man's height is relatively taller (because a higher z - score means the value is relatively closer to or above the mean in terms of standard deviations)

Answer:

s:
(a) \(z = 0.75\)

(b) \(z\approx - 1.42\)

Question 8: The American man