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Elementary Statistics 11th

Robert Johnson, Patricia Kuby

Chapter 6

Normal Probability Distributions

Educators

AZ

Problem 1

a. Explain why the IQ score is a continuous variable.
b. What are the mean and the standard deviation for the distribution of: IQ scores? SAT scores? standard scores?
c. Express, algebraically or as an equation, the relationship between standard scores and IQ scores and the relationship between standard scores and SAT scores.
d. What standard score is 2 standard deviations above the mean? What IQ score is 2 standard deviations above the mean? What SAT score is 2 standard deviations above the mean?
e. Compare the information about percentage of distribution, in Figure A on page $268,$ with the empirical rule studied in Chapter $2 .$ Explain the similarities.

AZ
Ashley Z.
Numerade Educator

Problem 2

Examine the intelligence quotient, or IQ, as it is defined by the formula:
Intelligence Quotient $=100 \times$ (Mental Age/Chronological Age)
Justify why it is reasonable for the mean to be 100.

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Problem 3

Percentage, proportion, or probability-identify which is illustrated by each of the following statements.
a. One-third of the crowd had a clear view of the event.
b. Fifteen percent of the voters were polled as they left the voting precinct.
c. The chance of rain during the day tomorrow is 0.2.

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Problem 4

Percentage, proportion, or probability-in your own words, using between 25 and 50 words for each, describe how:
a. percentage is different from the other two.
b. proportion is different from the other two.
c. probability is different from the other two.
d. all three are basically the same thing.

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