Average height of adult men

Question

Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of -0.39. Round your answer to one decimal place.

Answer 1

Hi Bailey,

Imagine you're in a room filled with adult men, and you're curious about the height of a particular individual. Well, you're in luck because we can use some statistical magic to figure that out.



First, we need to understand the concept of a z-score. A z-score tells us how many standard deviations a particular value is away from the mean (average). In this case, we have an average height of 69.0 inches and a standard deviation of 2.8 inches.

Now, you mentioned a z-score of -0.39. This means that the height we're interested in is 0.39 standard deviations below the average.

To find the height of this man, we'll do a little calculation:

Height = Mean + (Z-Score * Standard Deviation)

Height = 69.0 inches + (-0.39 * 2.8 inches)

Height = 69.0 inches - 1.092 inches

Height ≈ 67.9 inches

So, a man with a z-score of -0.39 has an estimated height of approximately 67.9 inches. Rounded to one decimal place, that's 67.9 inches.

There you have it, a simple yet powerful way to estimate the height of a man using statistics and z-scores. Happy measuring!

Thank you,

Benjamin M.

Answer 2

Hi Bailey,

This is once again a case for the classic equation z=x-mu/sigma. Here, you are given z, so:

z= -0.39

x= x, the height you're looking for

mu=69.0 in.

sigma=std. deviation=2.8 in.

Thus:

-0.39=(x-69.0)/2.8

Multiply both sides by 2.8:

-1.092=x-69.0

Add 69.0 on both sides

x=67.908; to one decimal:

x=67.9 inches