Chapter 3.1, Problem 3.15E

(a)

To determine

To explain the mean of 90^th percentile of cholesterol level.

Explanation of Solution

Given:

State	Percent	State	Percent	State	Percent
Alabama	5.3	Louisiana	5.2	Ohio	7.2
Alaska	6.8	Maine	5.6	Oklahoma	3.8
Arizona	5.9	Maryland	4.6	Oregon	6.4
Arkansas	4.9	Massachusetts	5.2	Pennsylvania	5.7
California	7.7	Michigan	8.7	Rhode Island	8.8
Colorado	5.2	Minnesota	5.9	South Carolina	7.3
Connecticut	6.1	Mississippi	7.8	South Dakota	3.2
Delaware	4.8	Missouri	6.4	Tennessee	7.2
Florida	6.6	Montana	4.6	Texas	5.1
Georgia	6.5	Nebraska	3.5	Utah	3.5
Hawaii	4.5	Nevada	7.3	Vermont	5.2
Idaho	5	New Hampshire	4.1	Virginia	4.3
Illinois	6.9	New Jersey	5.8	Washington	5.8
Indiana	6.2	New Mexico	4	West Virginia	4.5
Iowa	4.2	New york	5.8	Wisconsin	5
Kansas	4.8	North Carolina	7	Wyoming	3.3
Kentucky	7.1	North Dakota	3.6

Graph:

The histogram:

  

(b)

To determine

To calculate the summaries of the given data set.

Explanation of Solution

Calculation:

The summary of the given dataset is given below:

Descriptive statistics	Percent
count	50
mean	5.5980
sample variance	1.9349
sample standard deviation	1.3910
minimum	3.2
maximum	8.8
range	5.6
1st quartile	4.6000
median	5.4500
3rd quartile	6.5750
interquartile range	1.9750
mode	5.2000

For the shape of the given data:

  

Based on the given box plot it can be easily observed that the given data is right skewed as the tail of the distribution is towards the right side. Therefore, it is right skewed dataset.

(c)

To determine

To calculate the percentile for the Illinois.

Answer to Problem 3.15E

80^th percentile

Explanation of Solution

Calculation:

  $\begin{array}{c}\text{Percentile = }\frac{\text{No}\text{. of countries less and equal to Illinois}}{\text{Total no}\text{. of countries}}\times 100\\ =\frac{40}{50}\times 100\\ =80\end{array}$