Question

the average resting heart rate of a population is 90 beats per minute, with a standard deviation of 11 bpm. find the z - scores that correspond to each of the following heart rates. round your answers to the nearest hundredth, if necessary. (a) 120 bpm z = (b) 75 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) - 120 bpm

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 mean of the population, and $\sigma$ is the standard deviation of the population. Here, $\mu = 90$, $\sigma=11$, and $x = 120$.

Step2: Substitute values into formula

Substitute $x = 120$, $\mu=90$, and $\sigma = 11$ into the formula: $z=\frac{120 - 90}{11}=\frac{30}{11}\approx2.73$

Part (b) - 75 bpm

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 mean of the population, and $\sigma$ is the standard deviation of the population. Here, $\mu = 90$, $\sigma = 11$, and $x=75$.

Step2: Substitute values into formula

Substitute $x = 75$, $\mu = 90$, and $\sigma=11$ into the formula: $z=\frac{75 - 90}{11}=\frac{- 15}{11}\approx - 1.36$

Question 8

Step1: Calculate z - score for American man

For the American man, $\mu_{A}=177$, $\sigma_{A}=7.4$, and $x_{A}=173$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$, we get $z_{A}=\frac{173 - 177}{7.4}=\frac{-4}{7.4}\approx - 0.54$

Step2: Calculate z - score for Indian man

For the Indian man, $\mu_{I}=165$, $\sigma_{I}=6.7$, and $x_{I}=153$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$, we get $z_{I}=\frac{153 - 165}{6.7}=\frac{-12}{6.7}\approx - 1.79$

Step3: Compare z - scores

We compare the z - scores of the two men. The z - score of the American man ($z_{A}\approx - 0.54$) is greater than the z - score of the Indian man ($z_{I}\approx - 1.79$). A higher z - score (less negative in this case) means that the American man's height is relatively taller compared to his national population.

Answer:

s:
(a) $z\approx\boldsymbol{2.73}$

(b) $z\approx\boldsymbol{-1.36}$

Question 8: The American man