Challenge Problem In statistics, the standard normal density function is given by f ( x ) = 1 2 π ⋅ exp [ − x 2 2 ] . This function can be transformed to describe any general normal distribution with mean μ , and standard deviation, σ . A general normal density function is given by f ( x ) = 1 2 π ⋅ σ ⋅ exp [ − ( x − μ ) 2 2 σ 2 ] . Describe the transformations needed to get from the graph of the standard normal function to the graph of a general normal function.
Challenge Problem In statistics, the standard normal density function is given by f ( x ) = 1 2 π ⋅ exp [ − x 2 2 ] . This function can be transformed to describe any general normal distribution with mean μ , and standard deviation, σ . A general normal density function is given by f ( x ) = 1 2 π ⋅ σ ⋅ exp [ − ( x − μ ) 2 2 σ 2 ] . Describe the transformations needed to get from the graph of the standard normal function to the graph of a general normal function.
Solution Summary: The author explains the transformations needed to graph the general normal function f(x)=1sqrt
Challenge Problem In statistics, the standard normal density function is given by
f
(
x
)
=
1
2
π
⋅
exp
[
−
x
2
2
]
. This function can be transformed to describe any general normal distribution with mean
μ
,
and standard deviation,
σ
. A general normal density function is given by
f
(
x
)
=
1
2
π
⋅
σ
⋅
exp
[
−
(
x
−
μ
)
2
2
σ
2
]
. Describe the transformations needed to get from the graph of the standard normal function to the graph of a general normal function.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Points z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
A curve, described by x2 + y2 + 8x = 0, has a point A at (−4, 4) on the curve.Part A: What are the polar coordinates of A? Give an exact answer.Part B: What is the polar form of the equation? What type of polar curve is this?Part C: What is the directed distance when Ø = 5pi/6 Give an exact answer.
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