Chapter 5.4, Problem 237E

The distribution of incomes as of 2012 in the United States in $5000 increments is given in the following table. The kth row denotes the percentage of households with incomes between $5000xk and 5000 xk +4999. The row k = 40 contains all households with income between $200,000 and $250,000 and k = 41 accounts for all households with income exceeding $250,000.

0	3.5	21	1.5
1	4.1	22	1.4
2	5.9	23	1.3
3	5.7	24	1.3
4	5.9	25	1.1
5	5.4	26	1.0
6	4.4	27	0.75
7	4.1	28	0.8
8	4.8	29	1.0
9	4.1	30	0.6
10	4.3	31	0.6
11	3.5	32	0.5
12	3.7	33	0.5
13	3.2	34	0.4
14	3.0	35	0.3
15	2.8	36	0.3
16	2.5	37	0.3
17	2.2	38	0.2
18	2.2	39	1.8
19	1.8	40	2.3
20	2.1	41

Table 5.8 Income Distributions Source: http: //www. census.gov/prod/2013 pubs/p60-245.pdf

a.

Estimate the percentage of U.S households in 2012 with incomes less than $55,000.

b.

What percentage of households had incomes exceeding $85,000?

c.

Plot the data and try to fit its shape to that of a graph of the form $a\left(x+c\right)e^{-b\left(x+e\right)}$ for suitable a, b, c.