Question

1. The following table gives data on the US population based on age. In the far right column, create a probability model for this data and indicate how you know that the model is a valid assignment of probabilities. Suggestion: To simplify the computation, you could copy and paste this table into an Excel sheet and do the calculation there. To the right of the table, show what calculations was done on a calculator to get each answer or show what formula was used in Excel and how all calculations were completed.

2008 Income of US Families
Class Interval	Number (in thousands)	Probabilities
< $25,000	28,943.7
$25,000 - $49,999	29,178.1
$50,000 - $74,999	20,975.4
$75,000-$99,999	13,944.5
> $100,000	24,022.1
Total Number of Families	117,063.8

Answer 1

To calculate the probabilities of each class interval, we need to divide the number for each class interval with Total Number of Families (117,063.8).

Let the number 117,063.8 be in Cell B8 after copying into excel as shown in the screenshot.

Then,

Probabilities for Class Interval < $25,000 = 28,943.7 / 117,063.8 = 0.2472472

Using excel, typing the formula =B3/B8 in cell C3, we get the answer as 0.247247228

Probabilities for Class Interval $25,000 - $49,999 = 29,178.1 / 117,063.8 = 0.2492496

Using excel, typing the formula =B4/B8 in cell C4, we get the answer as 0.249249555

Probabilities for Class Interval $50,000 - $74,999 = 20,975.4 / 117,063.8 = 0.1791792

Using excel, typing the formula =B5/B8 in cell C5, we get the answer as 0.179179217

Probabilities for Class Interval $75,000-$99,999 = 13,944.5 / 117,063.8 = 0.1191188

Using excel, typing the formula =B6/B8 in cell C6, we get the answer as 0.119118805

Probabilities for Class Interval > $100,000 = 24,022.1 / 117,063.8 = 0.2052052

Using excel, typing the formula =B7/B8 in cell C7, we get the answer as 0.205205196

Sum of all probabilities = 0.247247228 + 0.249249555 + 0.179179217 + 0.119118805 + 0.205205196 = 1

Since the sum of all probabilities is 1 , the model is a valid assignment of probabilities