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How much vitamin C do you need? The Food and Nutrition
Chapter , Problem 1.169(choose chapter or problem)
How much vitamin C do you need?
The 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. 47 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 women aged 19 to 30 years, the EAR is 60 milligrams per day (mg/d), the RDA is 75 mg/d, and the UL is 2000 mg/d. 48
(a) 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.
(b) Sketch the distribution of vitamin C requirements for 19- to 30-year-old women. Mark the EAR, the RDA, and the UL on your plot.
Questions & Answers
QUESTION:
How much vitamin C do you need?
The 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. 47 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 women aged 19 to 30 years, the EAR is 60 milligrams per day (mg/d), the RDA is 75 mg/d, and the UL is 2000 mg/d. 48
(a) 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.
(b) Sketch the distribution of vitamin C requirements for 19- to 30-year-old women. Mark the EAR, the RDA, and the UL on your plot.
ANSWER:Step 1 of 2
(a)
It’s given that the Researchers assumed that the distribution of requirements for vitamin C is Normal. And The EAR gives the mean, ie;
Mean, \(\mu=60 \mathrm{mg} / \mathrm{d}\)
It’s given that the recommended dietary allowance (RDA) for women aged 19 to 30 years is 75mg/d.
Let’s assume to be 97.72 percentile. That means the vitamin C requirement normal distribution proportion is 97.72. Then, the z-score corresponding to 97.72 percentile is 2.0 (From TABLE A Standard Normal probabilities)