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.
3. Consider the following theorem:
Theorem: If n is an odd integer, then n³ is an odd integer.
Note: There is an implicit universal quantifier for this theorem. Technically we could write:
For all integers n, if n is an odd integer, then n³ is an odd integer.
(a) Explore the statement by constructing at least three examples that satisfy the hypothesis,
one of which uses a negative value. Verify the conclusion is true for each example. You
do not need to write your examples formally, but your work should be easy to follow.
(b) Pick one of your examples from part (a) and complete the following sentence frame:
One example that verifies the theorem is when n =
We see the hypothesis is
true because
and the conclusion is true because
(c) Use the definition of odd to construct a know-show table that outlines the proof of the
theorem. You do not need to write a proof at this time.
matrix 4
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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