The heights of American women between the ages of 18 and 24 are approximately normally distributed. The mean is 64.1 inches, and the standard deviation is 2.5 inches.

What percentage of such women are over 5 feet 8 inches tall?

z = (68 - 64.1)/2.5 = + 1.56
= P(z > 1.56) (100)
= 0.0594 (100)
= 5.9%
But 5.9% is marked as wrong still. Any ideas?

bam

Well, it seems like there's a little bit of a height discrepancy going on here. You see, 5 feet 8 inches is equivalent to 68 inches, not 58 inches. So, let's work that out again, shall we?

Now, we need to find the percentage of women who are taller than 68 inches. To do that, we'll calculate the z-score:

z = (68 - 64.1) / 2.5
= 1.56

So, we want to find P(z > 1.56). Looking it up in a standard normal distribution table, we find that the percentage is approximately 6.3%.

Therefore, approximately 6.3% of women between the ages of 18 and 24 are over 5 feet 8 inches tall. Just remember to double-check those measurement conversions!

To find the percentage of women who are over 5 feet 8 inches tall, we first need to convert this height into inches.

5 feet 8 inches is equal to (5 * 12) + 8 = 68 inches.

Next, we calculate the z-score corresponding to a height of 68 inches using the formula:

z = (x - μ) / σ

where x is the height, μ is the mean, and σ is the standard deviation.

Using the given values, we have:

z = (68 - 64.1) / 2.5 = 1.56

Now, we want to find the probability of a woman being taller than 68 inches, which is equivalent to finding the probability of z being greater than 1.56.

Using a standard normal distribution table or a calculator, we can find that the probability of z being greater than 1.56 is approximately 0.0594, or 5.94%.

So, the correct answer is indeed 5.94%.

If your answer of 5.9% is marked as wrong, there could be a rounding error or a slight difference in the table or calculator you are using. Double-check your calculations, and consider rounding to an additional decimal place to see if that resolves the discrepancy.

wrong answer. I still don't know how to solve but per my key answer it is 5.5%

I get 5.94%, but you are correct. Bogus answer key.