Table 1

Intelligence Quotient

IQ	Norm Distribution	Z-scores
55	0.0028	-2.0588
82	0.0210	-0.4706
84	0.0221	-0.3529
93	0.0231	0.1765
95	0.0225	0.2941
97	0.0216	0.4117
97	0.0216	0.4117
100	0.0197	0.5882
107	0.0142	1.0000
110	0.0117	1.1765

Table 2

Intelligence Quotient

IQ

Norm Distribution

Z-scores

55

0.0003

-3

82

0.0129

-1.2

84

0.0151

-1.0667

93

0.0239

-0.4667

95

0.0252

-0.3333

97

0.0261

-0.2

97

0.0261

-0.2

100

0.0266

0

107

0.0239

0.4667

Using the IQ variable, Tables 1 and 2.

Table 1, 10 scores with IQ Variables with = 90 with the = 17 transform x into Z scores.

Table 2 compare the IQ, the same 10 scores, to the national average of =100 with = 15 for the students. Transform x into a Z scores.

Part 2:

Explain why transforming x values into z-scores is helpful using the example of the problem I solved in Part 1.

Why knowing the z-scores for IQ helps you to understand the standard normal distribution of these scores for the math class. How z-scores can help researchers use the data from a sample to make inferences about a population.

How does converting the IQ scores (x-score) to the more familiar metric IQ scores (z-scores) in the second column can be helpful for the students in the math class?