Assume a standardized IQ test exists that possesses a normal distribution and has a mean score of 100 with a standard deviation of 5 What is the probability of selecting someone from the general population at random who would: The following is a list of z-scores for two different IQ tests. The table on the LEFT is for an IQtest with a mean score of 100 and a Standard Deviation (SD) of 10. The table on the RIGHTis for an IQ test with a mean score of 100 and a SD of 5.IQ Scorez-Score75 -2.576 -2.477 -2.378 -2.279 -2.180 -2.081 -1.982 -1.883 -1.784 -1.685-1.586 -1.487-1.388 -1.289-1.190 -1.091 -0.992 -0.893 -0.794 -0.695 -0.596 -0.497-0.398 -0.299 -0.1100 0101 0.1102 0.2103 0.3104 0.4105 0.5106 0.6107 0.7108 0.8109 0.9110 1.0111 1.1112113 1.3114 1.4115 1.5IQ Score75767778798081828384858687888990919293949596979899100101102103104105106107108109110111113114115z-Score-5.0-4.8-4.6-4.4-4.2-4.0-3.8-3.6-3.4-3.2-3.0-2.8-2.6-2.4-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.200.20.40.60.81.01.21.41.61.82.02.22.42.6№2.83.0 15. Score 104 or lower?16. Score 104 or higher?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume a standardized IQ test exists that possesses a normal distribution and has a mean score of 100 with a standard deviation of 5

What is the probability of selecting someone from the general population at random who would:

The following is a list of z-scores for two different IQ tests. The table on the LEFT is for an IQ
test with a mean score of 100 and a Standard Deviation (SD) of 10. The table on the RIGHT
is for an IQ test with a mean score of 100 and a SD of 5.
IQ Score
z-Score
75 -2.5
76 -2.4
77 -2.3
78 -2.2
79 -2.1
80 -2.0
81 -1.9
82 -1.8
83 -1.7
84 -1.6
85
-1.5
86 -1.4
87
-1.3
88 -1.2
89
-1.1
90 -1.0
91 -0.9
92 -0.8
93 -0.7
94 -0.6
95 -0.5
96 -0.4
97
-0.3
98 -0.2
99 -0.1
100 0
101 0.1
102 0.2
103 0.3
104 0.4
105 0.5
106 0.6
107 0.7
108 0.8
109 0.9
110 1.0
111 1.1
112
113 1.3
114 1.4
115 1.5
IQ Score
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
113
114
115
z-Score
-5.0
-4.8
-4.6
-4.4
-4.2
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
№
2.8
3.0

15. Score 104 or lower?
16. Score 104 or higher?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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