Question

Section 1.

IQ tests supposedly measure our intelligence. They typically are ‘normed’ so that they have a mean of 100 and a standard deviation of 15. (Higher scores show higher intelligence.)

Use the graph and use the z-score and percents from columns b and c in Table A, when relevant.
Questions

If you scored 140, what is your z-score? (Interpret.)

Use table A and use the graph
Group of answer choices
A 2.80 z. I'm at the 99.74 percentile rank and 0.26% of people scored smarter than me.
B -2.80 z. I'm at the 0.26 percentile rank and 99.74% of people scored smarter than me.
C 2.67 z. I'm at the 99.62 percentile rank and 0.38% of people scored smarter than me.
D. 2.67 z. I'm at the 0.38 percentile rank and 99.62% of people scored smarter than me.
E. 2.80 z. I'm at the 0.26 percentile rank and 99.74% of people scored smarter than me.
F. -2.67 z. I'm at the 0.38 percentile rank and 99.62% of people scored smarter than me.
G. -2.67 z. I'm at the 99.62 percentile rank and 0.38% of people scored smarter than me.
H. -2.80 z. I'm at the 99.74 percentile rank and 0.26% of people scored smarter than me.

If your cousin scored 58, what would you be able to tell them about how they compare to others who took the test? (Interpret) Group of answer choices

2.67 z. They are at the 99.62 percentile rank and 0.38% of people scored smarter than them.

B. 2.67 z. They are at the 0.37 percentile rank and 99.62% of people scored smarter than them.
C. -2.80 z. They are at the 99.74 percentile rank and 0.26 % of people scored smarter than them.
D 2.80 z. They are at the 0.26 percentile rank and 99.74% of people scored smarter than them.
E. 2.80 z. They are at the 99.74 percentile rank and 0.26 % of people scored smarter than them.
F. -2.80 z. They are at the 0.26 percentile rank and 99.74% of people scored smarter than them.
G. -2.67 z. They are at the 99.62 percentile rank and 0.38% of people scored smarter than them.
H. -2.67 z. They are at the 0.37 percentile rank and 99.62% of people scored smarter than them.

Answer 1

Solution:
Given in the question
Mean () = 100
Standard deviation () = 15
Solution(a)
If X = 140
Than Z-score can be calculated as
Z-score = (X-)/ = (140-100)/15 = 2.67
Z-score = 2.67 at X = 140
From Z table we found p-value
P(X<=140) = 0.9962
and P(X>140) = 1 - P(X<=140) = 1 - 0.9962 = 0.0038
So Its correct answer is C. i.e. Z-score = 2.67, i am at the 99.62% rank and 0.38% of people are scored smarter than me.
Solution(b)
Here X= 58
Than Z= (58-100)/15 = -2.8
From Z table we found a p-value
P(X<58) = 0.0026
P(X>58) = 1- 0.0026 = 0.9974
So its answer is F i.e. Z = -2.80, they are at the 0.26% percentile rank and 99.74% of people scored smarter than them.