Question

37. 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 150-cm Indian man? The American man The Indian man

Answer 1

The American man

Step-by-step explanation

To find the man that is taller relative to his nationality, we have to find the z-score of both men. The z-score represents how far away from the mean that a data value is.

To find the z-score, apply the formula:

`z=(x-\mu)/(\sigma)`

where x = data value; μ = mean; σ = standard deviation

For the American man, the z-score is:

`\begin{gathered} z=(173-177)/(7.4) \\ z=(-4)/(7.4) \\ z=-0.541 \end{gathered}`

For the Indian man, the z-score is:

`\begin{gathered} z=(150-165)/(6.7) \\ z=(-15)/(6.7) \\ z=-2.239 \end{gathered}`

We see that the American man has a height with a z-score higher than that of the Indian man.

This means that the American man is taller than the Indian man relative to their nationalities.