statistics word problem help

Question

Cholesterol levels in the American adult population have approximately a bell shaped distribution with a mean 170 and standard deviation 6.9. A "healthy" level is one that falls within the range of 95% of all cholesterol levels. What is the largest "healthy" cholesterol?

Answer 1

Daniella,

 

The wording here "falls within the range of 95%" hints at the assumption that samples in a bell shaped distribution gravitate toward the mean and calculates confidence intervals based on a mean and a standard deviation in the form μ+/-σ where mu is the mean and sigma is the standard deviation. The lower limit is μ-σ and the upper, μ+σ.

 

Some call it the 68-95-99.7 rule because everything within one sigma, or standard deviation of the mean, encompasses 68% of the total population. Realize this is approximate. It's actually 68.27%. Likewise everything within two standard deviations away from the mean is 95% (it's more like 95.45%). Everything three standard deviations away from the mean would cover 99.7% (in real life 99.73%). You can calculate something similar for four and five sigma to get closer to 100% of the range.

 

In this case the problem is asking for the upper limit of the 95% confidence interval which is two sigma away so just calculate μ+2σ or 170+2*6.9=183.8. Hope that helps!