image 1.157 How much vitamin C do women consume? To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:44

Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.1 31 42 48 61 79 102 126 142 179

  1. (a) Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean and standard deviation of this distribution assuming that the distribution is Normal. Explain your method for doing this.

  2. (b) Sketch your Normal intake distribution on the same graph with a sketch of the requirement distribution that you produced in part (b) of Exercise 1.155.

  3. (c) Do you think that many women aged 19 to 30 years are getting the amount of vitamin C that they need? Explain your answer.