Question

The cholesterol levels of a group of young women at a university are normally distributed, with a mean of 187 and a standard deviation of 40. What percent of the young women have the following cholesterol levels? (Round your answers to one decimal place.

(a) greater than 215

(b) between 190 and 223

show your work

Answer 1

[AI-generated answer — Bot GPT 3.5]

(a) To find the percentage of young women with cholesterol levels greater than 215, we first need to find the z-score for 215:

z = (215 - 187) / 40
z = 28 / 40
z = 0.7

Using a standard normal table or calculator, we can find that the percentage of the area to the right of z = 0.7 is approximately 0.7580. So, 75.8% of young women have cholesterol levels greater than 215.

(b) To find the percentage of young women with cholesterol levels between 190 and 223, we first need to find the z-scores for 190 and 223:

For 190:
z = (190 - 187) / 40
z = 3 / 40
z = 0.075

For 223:
z = (223 - 187) / 40
z = 36 / 40
z = 0.9

Using a standard normal table or calculator, we can find the area to the right of z = 0.075 (approximately 0.4721) and the area to the right of z = 0.9 (approximately 0.8159). To find the area between these z-scores, we subtract the smaller area from the larger area:

0.8159 - 0.4721 = 0.3438

So, approximately 34.4% of young women have cholesterol levels between 190 and 223.