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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 51is 18milligrams (mg) per day. The iron intakes during a 24-hour period for a random sample of45 adult females under the age of 51have a mean of 14.7mgand standard deviation of 3.1mg.

a. Construct a graph .
b. Apply Chebyshev's rule with k=2 to make pertinent statements about the observations in the sample.
c. Repeat part (b) with k=3.

Short Answer

Expert verified

Part(a) Required figure is given below.

Part(b) At least 34adult females have recommended dietary allowance (RDA) of iron
Part(c) At least 40adult females have recommended dietary allowance (RDA) of iron.

Step by step solution

01

Part(a) Step 1 : Given information

We are given that sample has 45adult females.

Mean x=14.7

Standard deviation s=3.1

02

Part(a) Step 2 : Simplify

According to chebyshev's Rule

x=14.7x-s=11.6x-2s=8.5x-3s=5.4x+s=17.8x+2s=20.9x+3s=24.0

Required graph is

03

Part(b) Step 1 : Given information

We are given that sample has 45adult females

Mean x=14.7

Standard deviation s=3.1

04

Part(b) Step 2 : Simplify

According to Chebyshev's rule ,if

k=2, then at least 75%of the adult females in the sample within two standard deviations to either side of the mean.

Now,

45×0.75≈34

Now, two standard deviations to either side of the mean is from

8.5to 20.9milligram.

Interpretation- At least 34out of 45adult females in the sample have recommended dietary allowances of iron between 8.5mgand 20.9mg

05

Part(c) Step 2 : Given information

We are given that sample has 45adult females.

Meanx=14.7

Standard deviation s=3.1

06

Part(c) Step 2 : Simplify

According to Chebyshev's rule ,if

k=3, then at least 89%of the adult females are within two standard deviations to either side of the mean.

Now,

45×0.89≈40

Now, two standard deviations to either side of the mean is from

5.4to 24.0.

Interpretation- At least 40out of 45adult females in the sample have recommended dietary allowance of iron between 5.4mg and 24.0mg

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