THe distribution of cholesterol levels in teenage boys is approximately normal with a mean of 170 and a standard deviation of 30. Levels above 200 warrant attention. What percentage of teenage boys have levels between 170 and 225?
2007-02-27 14:14:34 · 3 answers · asked by nessa 1 in Education & Reference ➔ Homework Help
find the z-score by puting the 170 (the mean)-225 (the value we want to get to) over 30 (standard deviation) and now you have a z value and now subtract .5 (the z value of 170) to know how many are between there.
2007-02-27 14:21:23 · answer #1 · answered by Zach D 2 · 0⤊ 0⤋
Imagine a bell curve, where the mean is smack dab in the middle, and values are equally distributed left and right of it. The normalized (or "Gaussian" to be technical) distribution says that 68% of data is within 1 standard deviation from that mean (left and right) and that 95% is within 2, and 99% is within 3. So we want to know how many standard deviations from the mean 225 is. 225 is about 55 units from the mean. Since one standard deviation is 30, that's about 2 standard deviations. So how do we do the percent above the mean?
Since 95% total are within 2 standard deviations, then you can split that value in half, because aroound 47.5% will be below the mean and 47.5% above it. Since we're just under 2 standard deviations, a good estimate is that about 47% are between 170 (the mean) and 225.
2007-02-27 14:25:40 · answer #2 · answered by bloggerdude2005 5 · 0⤊ 0⤋
A bit of very simple math can give you the answer. Your numbers may be "statistics", but your problem is plain ol' simple arithmetic. God Bless you.
2007-02-27 14:23:31 · answer #3 · answered by ? 7 · 0⤊ 0⤋