Psychology. A test devised to measure aggressive-passive personalities was standardized on a large group of people. The scores were normally distributed with a mean of 50 and a standard deviation of 10 . If we designate the highest 10 % as aggressive, the next 20 % as moderately aggressive, the middle 40 % as average, the next 20 % as moderately passive, and the lowest 10 % as passive, what ranges of scores will be covered by these five designations?
Psychology. A test devised to measure aggressive-passive personalities was standardized on a large group of people. The scores were normally distributed with a mean of 50 and a standard deviation of 10 . If we designate the highest 10 % as aggressive, the next 20 % as moderately aggressive, the middle 40 % as average, the next 20 % as moderately passive, and the lowest 10 % as passive, what ranges of scores will be covered by these five designations?
Solution Summary: The author calculates the range of scores covered by the five designations with mean 50 and standard deviation 10.
Psychology. A test devised to measure aggressive-passive personalities was standardized on a large group of people. The scores were normally distributed with a mean of
50
and a standard deviation of
10
. If we designate the highest
10
%
as aggressive, the next
20
%
as moderately aggressive, the middle
40
%
as average, the next
20
%
as moderately passive, and the lowest
10
%
as passive, what ranges of scores will be covered by these five designations?
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.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
show your answer in
pen and paper
Don't use any Al tool
show ur answer in pe
n and paper then take
-2-i
Evaluate f² (3xy + iy²)dz
a) along the straight line joining from z = i to z = 2 - i
Inspiring Excellence
b) along the parabola from x = 2t - 2 and y = 1+t-t²
Chapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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