Using the normal distribution to determine proportions, percentiles, and percent
ID: 3257120 • Letter: U
Question
Using the normal distribution to determine proportions, percentiles, and percentile ranks Flavonoids found in green, black, or white tea may reduce the risk of heart disease by decreasing low-density lipoproteins, also known as LDL or bad cholesterol. A health psychologist is interested in helping her patients with bad cholesterol make good lifestyle choices. Low-density lipoprotein levels follow a normal distribution with mu = 100 and sigma = 32. Use the Distributions tool to help answer the questions that follow. The minimum z-score necessary to be in the highest 5% of the low-density lipoprotein distribution is z = ____. Use this z-score to determine X, the corresponding low-density lipoprotein level. X = This score, X, is the ____ percentile of low-density lipoprotein levels among people. The percentile rank of this score is ____. Low-density lipoprotein levels between 130 and 159 are considered to be borderline high. What percentage of people have LDLs in this range? 16.86% 12.45% 14.07% 1.14% What percentage of people have the optimal level of LDLs (a level below 100)? 1.14% 20% 40% 50%Explanation / Answer
Highest 5% is the 95th percentile of N(100,322)
Z score = 1.644853
Corresponding X score = 52.6353 , which is the 95th percentile and the percentile rank is 95.
% of people with LDL in the range 130 -159 is 14.07%.
% of people with optimal level of LDL (<100 ) is50%
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