Question

iron is essential to most life forms and to normal human physiology. it is an integral part of many proteins and enzymes that maintain good health. recommendations for iron are provided in dietary reference intakes, developed by the institute of medicine of the national academy of sciences. the recommended dietary allowance (rda) of iron for adult females under the age of 51 is 18 milligrams (mg) per day. the iron intakes during a 24 - hour period for a random sample of 45 adult females under the age of 51 have a mean of 14.7 mg and a standard deviation of 3.7 mg. complete parts (a) through (c) below.
a. construct a graph that shows the mean and one, two, and three standard deviations to either side of the mean.
\\(\bar{x}-3s\\) \\(\bar{x}-2s\\) \\(\bar{x}-s\\) \\(\bar{x}\\) \\(\bar{x}+s\\) \\(\bar{x}+2s\\) \\(\bar{x}+3s\\)
(type integers or decimals rounded to one decimal place as needed.)

Explanation:

Step1: Identify the mean and standard - deviation values

Given $\bar{x}=14.7$ mg and $s = 3.7$ mg.

Step2: Calculate $\bar{x}-3s$

$\bar{x}-3s=14.7-3\times3.7=14.7 - 11.1 = 3.6$

Step3: Calculate $\bar{x}-2s$

$\bar{x}-2s=14.7-2\times3.7=14.7 - 7.4 = 7.3$

Step4: Calculate $\bar{x}-s$

$\bar{x}-s=14.7-3.7 = 11.0$

Step5: Calculate $\bar{x}+s$

$\bar{x}+s=14.7 + 3.7=18.4$

Step6: Calculate $\bar{x}+2s$

$\bar{x}+2s=14.7+2\times3.7=14.7 + 7.4 = 22.1$

Step7: Calculate $\bar{x}+3s$

$\bar{x}+3s=14.7+3\times3.7=14.7 + 11.1 = 25.8$

Answer:

3.6, 7.3, 11.0, 14.7, 18.4, 22.1, 25.8