Question

For a population with a mean of LaTeX: \muμ= 100 and a standard deviation of LaTeX: \sigmaσ=20, Find the X values that corresponds to each of the following z-scores: z = -.40 z = -.50 z= +1.80 z = +.75 z = +1.50

Answer #1

Population mean ( ) = 100

Standard deviation ( ) = 20

Formula for the z score is as follows

Z =

Therefore

x = z + ---------(i)

Using this evaluation we can calculate the value of x.

1.For z = - 0.40

x = z +

= ( - 0.40 )( 20 ) + 100

= - 8 + 100

= 92

** **x = 92

2. For z = - 0.50

x = ( - 0.50 ) ( 20 ) + 100

= - 10 + 100

= 90

x = 90

3. For z = + 1.80

x = ( 1.80) (20) +100

= 36 + 100

= 136

x = 136

4. For z = + 0.75

x = (0.75) (20) + 100

= 15 + 100

= 115

x = 115

5. For z = + 1.50

x = (1.50) (20) + 100

= 30 + 100

= 130

x = 130

For a population with a mean of u = 100 and a standard deviation
of o = 20
a. Find the z-score for each of the following X values.
X = 108 X = 115 X = 130
X = 90 X = 88 X = 95
b. Find the score ( X value) that corresponds to each of the
following z-scores.
z = -0.40 z = -0.50 z = 1.80
z = 0.75 z = 1.50 z = -1.25

A distribution of scores has a mean of LaTeX: \muμ= 80. If your
score is X = 72, which standard deviation would give you a better
grade: LaTeX: \sigmaσ= 4 or LaTeX: \sigmaσ= 6? If your score is X =
90, which standard deviation would give you a better grade: LaTeX:
\sigmaσ= 5 or LaTeX: \sigmaσ= 10?

1. Suppose an x distribution has mean LaTeX: \muμ= 10 and a
standard deviation of 2. Random sample sizes of 25 are drawn.
Describe the x-bar (mean of the sample) distribution and mean
and standard deviation of the distribution.
Find the z-values and the probability that x-bar will be between
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4.For a population with a mean of μ = 40 and σ = 11, find the
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will need to use a formula and a calculator to find these
values)
X = 45: z =_____ X = 52: z =_____X = 41: z =_____
X = 30: z =_____X = 25: z =_____X = 38: z =_____
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.0122 .0274 .3520 .0465

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of σ = 12.
a.For the population, find the z-score for each of the
following X values.
X = 69: z =_____X = 84: z =_____X = 63: z =_____
X = 54: z =_____X = 48: z =_____X = 45: z =_____
b.For the same population, find the score (X value) that
corresponds to each of the following z-scores.
z = 0.50: X=_____ z = 1.50:...

A sample has a mean of M =90 and a standard deviation
of s = 20 .
Find the z-score for each of the following X
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X = 95 X = 98 X = 105
X = 80 X = 88 X = 76
Find the X value for each of the following
z-scores.
z = -1.00 z = 0.50 z = -1.50
z = 0.75 z = -1.25 z = 2.60

a population with a mean of 65 and a standard deviation of 6 is
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. Find the z-score for each of the following X values. X = 80 X =
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True or False: a.) Variance is the mean of the squared deviation
score. b.) For any population, a z-score of +1.00 corresponds to a
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distribution with s=8, a score of X=64 corresponds to z=-.50. The
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