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STA 103 - Homework 1 Template
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- Consider the following list of Xi , Yi values:
Xi Yi
1 2
2 4
3 6
Using the above data, determine if the following equations are true or false.
(a)
q 5 XiYi = 5
q XiYi
(b)
q XiYi =
q Xi
q Yi
(c)
q (^) X 2 i 5 =^
1 5
q X
2 i
(d)
q ( Yi + 3) = (
q Yi ) + 3
(e) (
q Yi )^2 =
q Y (^) i^2
421482875 Salena (^) Duran
LAS [SXi^ Yi^
=5.1.
5(1.
+2.4 +3.6)
us: "...
= 148
1.2 +2.^
+3.
2"xzn
ee
sts"
isit
(s:[(yi +
+3) - (4 + 3)
Ras:
(2xic.3Teys.
(S([xi)
(^2) = (2 + 4 + b)
RHS -
-b L
- Suppose that tax paid by a certain person per year is denoted Ti , and is calculated using the following relationship to
that persons gross income ( Gi ):
Ti = 0_._ 25( Gi ≠ 10000)
(i.e, only people who have an income over $10,000 per year are taxed, and only the income beyond $10,000). You are
told that the total gross income for an area with 200 people is $6,000,000. Assume that all the people measured make
over $10,000 a year.
(a) Find the total taxes collected for the 200 people.
(b) Find
q (^1)
100
Ti for the 200 people.
(c) Find
q (2 Gi ≠ 40) for the 200 people.
+xX gross^
income
200 I (^) xi = 0.
i =^1
sand
Ti
in first
problem
X 200 "ori °^ to^
1,000,000)
I i = I i^
= 1
=
20
I (20i^
i =^1 the^200
people
↓
=^ 2(6,000,000)^
000,
so o
- In a population of 20 families, the number of cars owned by each family is given below:
Let X be the number of cars owned, and Xi be the possible values of X. Use this data to answer the following questions:
(a) Write down the relative-frequency distribution for X.
(b) Find the median of number of cars owned.
(c) Find the mean of number of cars owned.
(d) Using (b) and (c), are there more than 50% of values Xi above the mean, or less? Explain your answer.
n =^28
xi 012345
Freq. 14553
1 I^ [Freq =^20
xi) (^) oz exi:
8, 1,^ 1,^ 1,^ 1,^ 2,^ 1,^ 2,^ 1,^ 2,^ 3,^ 3,3,3,3,4,4,^ 4,^ 5,^
6
E
3 = 2.
sample mean:X:IEx:or^ (xi.^
f(xi)
I ·(i)
+ ()+^ 2(0)^
+3(2) +4(0)^
:^ s(20)^
+^ b0)
short^ wall
= 52
= 2.
The average number^ of
cars owned^ is
Since sayof
values fall below the median^ andsofall above
then more^
than so;^ fall^ below^ the^ mean^ since^ 2.5^ <2.
58% 58 E^ ->
fit
cell mean
- Suppose that a certain state has 794,000 people. Let the gross income for the i
th person be denoted by Gi , the taxes for
the i
th person be denoted Ti , and the disposable income for the i
th person be denoted Di.
Suppose that the mean gross income per year is $50,000, and the average taxes per year is $7500.
(a) If the individual disposable income is the gross income minus taxes, write down the equation for Di.
(b) Find the average disposable income per year for the entire state.
(c) Find the total taxes per year for the entire state, and the total gross income for year for the entire state.
(d) Find the total disposable income per year for the entire state.
-Ti
Di =^ $50,^
-744,
Total taxes^ per year ago
Total gross income^ per
year
root
o
total disposable^
income
80000000,
sasssoo
et
