Chapter 3.1, Problem 3.16E

(a)

To determine

To write a sentence about the actual unemployment rates in December and September 2008.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Actual percentage:}\\ \text{September 2008: 6}\text{.9\%}\\ \text{December 2008: 4}\text{.5\%}\end{array}$

The percentage of the September 2008 was higher than the December 2008, in September 2008 it was 6.9% and in December 2008 it was 4.5%.

(b)

To determine

To compare the percentile of the two months September and December 2008 for Illinois.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Mean = 4}\text{.5\%}\\ \text{Standard Deviation = 1\%}\end{array}$

Calculation:

The no. of countries less unemployment rates than Illinois are 42 and the total no. of countries are 42.

  $\begin{array}{c}\text{Percentile = }\frac{\text{No}\text{. of countries less and equal to Illinois}}{\text{Total no}\text{. of countries}}\times 100\\ =\frac{42}{50}\times 100\\ ={84}^{\text{th }}\text{percentile}\end{array}$

The unemployment percentile of Illinois is 80^th in September and in December it increases to 84^th percentile.

(c)

To determine

To calculate the percentile for the Illinois.

Answer to Problem 3.16E

September 2008: 3.43

December 2008: 1.03

Explanation of Solution

Formula used:

  $Z=\frac{x-\mu }{\sigma }$

Calculation:

The standard score of September 2008:

  $\begin{array}{c}z=\frac{6.9-3.47}{1}\\ =3.43\end{array}$

The standard score of December 2008:

  $\begin{array}{c}z=\frac{4.5-3.47}{1}\\ =1.03\end{array}$