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The basic formula we need is the Standard Normal Distribution formula (see related link) which is Z = (x - mean)/std dev. Solve for x, and we get: x = mean + z*std dev. From the Z table (see related link), area = 0.900 (your 90% in decimal form) we get the closest z value of 1.28 (from area = 0.8997). We can now solve for x, the value at the 90th percentile. X = 191 + (1.28)*22.4 or 219.672. Cholesterol, to my knowledge, is always given in whole numbers, so the value is 220 (rounded up).

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Q: Total cholesterol in children 10 to 15 years of age is assummed to follow a normal distribution with a mean of 191 amd a standard deviation of 22.4 what is the 90th percentile of total cholesterol?
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