The U.S. Food and Nutrition Board of the Institute of Medicine, working in coope

Question

The U.S. Food and Nutrition Board of the Institute of Medicine, working in cooperation with scientists from Canada, have used scientific data to answer this question for a variety of vitamins and minerals. Their methodology assumes that needs, or requirements, follow a distribution. They have produced guidelines called dietary reference intakes for different gender-by-age combinations. For vitamin C, there are three dietary reference intakes: the estimated average requirement (EAR), which is the mean of the requirement distribution; the recommended dietary allowance (RDA), which is the intake that would be sufficient for 97% to 98% of the population; and the tolerable upper level (UL), the intake that is unlikely to pose health risks. For men aged 14 to 18 years, the EAR is 63 milligrams per day (mg/d), the RDA is 75 mg/d, and the UL is 1,800 mg/d.

The researchers assumed that the distribution of requirements for vitamin C is normal. The EAR gives the mean. From the definition of the RDA, let's assume that its value is the 97.72 percentile. Use this information to determine the standard deviation of the requirement distribution.

Explanation / Answer

Mean = 63mg/d

97.72 percentile = 75 mg/d

P(X < A) = P(z < (A - mean)/standard deviation)

For 97.72, z value = 2

So, (75 - mean)/standard deviation = 2

(75 - 63)/ standard deviation = 2

So, standard deviation = (75-63)/2 = 6 mg/d

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