To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation (1) with σ = 5 and (A) μ = 8 (B) μ = 12 (C) μ = 16 Graph all three in the same viewing window with X min = − 10 , X max = 30 , Y min = 0 ,and Y max = 0.1 .
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation (1) with σ = 5 and (A) μ = 8 (B) μ = 12 (C) μ = 16 Graph all three in the same viewing window with X min = − 10 , X max = 30 , Y min = 0 ,and Y max = 0.1 .
Solution Summary: The author analyzes the equation of normal distribution f(x)=1sigma.
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean
µ
and standard deviation
σ
:
f
x
=
1
σ
2
π
e
−
x
−
μ
2
/
2
σ
2
Graph equation (1) with
σ
=
5
and
(A)
μ
=
8
(B)
μ
=
12
(C)
μ
=
16
Graph all three in the same viewing window with
X
min
=
−
10
,
X
max
=
30
,
Y
min
=
0
,and
Y
max
=
0.1
.
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
12:25 AM Sun Dec 22
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Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The
machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment
is closest to:
Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided.
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Multiple Choice
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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