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# The body mass index (BMI) of a person is defined to be the

ISBN: 9780073401331 38

## Solution for problem 3E Chapter 4.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

The body mass index (BMI) of a person is defined to be the person's body mass divided by the square of the person's height. The article "Influences of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle Deposition" (W. Bolch,  E. Farfan, et al„ Health Physics, 2001:378‒394) states that body mass index (in kg/m2) in men aged 25‒34 is log normally distributed with parameters μ = 3.215 and σ = 0.157.

a. Find the mean BMI for men aged 25‒34.

b. Find the standard deviation of BMI for men aged 25‒34.

c. Find the median BMI for men aged 25‒34.

d. What proportion of men aged 25‒34 have a BMI less than 22?

e. Find the 75th percentile of BMI for men aged 25‒34.

Step-by-Step Solution:
Step 1 of 3

Solution 3E

Step1 of 6:

Let us consider a random variable X it presents the BMI for randomly chosen man aged 25-34.

And X follows lognormal distribution with mean  and standard deviation

That is XN(3.215, 0.1572)

Here our goal is:

a).We need to find the mean BMI for men aged 25-34.

b).We need to find the standard deviation of BMI for men aged 25-34.

c).We need to find the median BMI for men aged 25-34.

d).We need to find the proportion of men aged 25.34 have a BMI less than 22.

e).We need to find the 75th percentile of BMI for men aged 25-34.

Step2 of 6:

a).

The probability density function of lognormal distribution is given by

Where,

mean

standard deviation

Z = standard normal variable.

Now, the mean BMI for men aged 25-34 is given by

=

=

=

= 25.0281

Hence, E(X) = 25.0281.

Step3 of 6:

b).

The Standard deviation of BMI for men aged 25-34 is given by

= 3.9497

Hence, =737.9516.

Step4 of 6:

c).

Here we need to find median of BMI for men aged 25-34. Let us consider “m” be the median lifetime of an electric component. And we know that median divides the data into two parts that is 0.5.

Now, median of BMI for men aged 25-34 is given by

We know that X N(3.215, 0.1572)

...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 3E from chapter: 4.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 3E from 4.6 chapter was answered, more than 452 students have viewed the full step-by-step answer. This full solution covers the following key subjects: AGED, Men, BMI, Find, Person. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “The body mass index (BMI) of a person is defined to be the person's body mass divided by the square of the person's height. The article "Influences of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle Deposition" (W. Bolch, E. Farfan, et al„ Health Physics, 2001:378?394) states that body mass index (in kg/m2) in men aged 25?34 is log normally distributed with parameters ? = 3.215 and ? = 0.157.a. Find the mean BMI for men aged 25?34.________________b. Find the standard deviation of BMI for men aged 25?34.________________c. Find the median BMI for men aged 25?34.________________d. What proportion of men aged 25?34 have a BMI less than 22?________________e. Find the 75th percentile of BMI for men aged 25?34.” is broken down into a number of easy to follow steps, and 120 words.

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