Question

1. In a normal population of IQ scores, what percent of people have “average” IQ’s?

Answer __68%

2. In a normal distribution, what percentage of people would be located at or below 2 standard deviations from the mean?

Answer _______70

3. Answer the following questions based on a distribution with a μ = 30 and σ = 5: ( don’t get this question )

1. What range of scores is considered “average”? ____________ to ______________

2. What percentage of people has an average score? __________________________

3. What percentage of people has extremely high or extremely low scores? _________

4. What range of scores (requires numbers to be noted in the blank spaces) have the highest probability of being selected? ____1______ to ___30______

Answer 1

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1. In a normal population of IQ scores, what percent of people have “average” IQ’s?The ones within 1 standard deviation from the mean have "average IQ". So, these are 68%, as 68% of the distribution is 1 standard deviation away from mean.

Answer __68%

2. In a normal distribution, what percentage of people would be located at or below 2 standard deviations from the mean? The area under the distribution 2 deviation away from mean is 5%, since 95% of area is under 2 deviations away from mean.

Answer _______5%

3. Answer the following questions based on a distribution with a μ = 30 and σ = 5: ( don’t get this question )

1. What range of scores is considered “average”? 30-5 = 25 to 30 + 5 = 35 or 25 to 30 ( 1 deviation away from mean)

2. What percentage of people has an average score? 68%, as explained above

3. What percentage of people has extremely high or extremely low scores? The ones having more than 2 deviation away from mean. As explained above, this is 5%

4. What range of scores (requires numbers to be noted in the blank spaces) have the highest probability of being selected? This depends on the question on how to define the "number with highest probability",  but we usually assume that anything above or below 2 deviation from the mean is an unusual event. Keeping that in mind, 2 deviation away from mean is 30-2*5 to 30+2*5 i.e. 20 to 40. Any number between 20 and 40 have highest probability to occur.