Question

9. The average IQ score is 100. The standard deviation is 15. If we assume IQ scores arenormally distributed: DRAW THE BELL CURVE!!a.What percentage of the population will have an IQ between 70 and 130?b. What range of scores would we consider unusually high?C.What percent of the population will have an IQ score within 3 standard deviations of the average IQ score?

Answer 1

The bell curve is shown below:

a)

We need to find the probability:

`P(70to find it we need to write in terms of z-scores given by:<p></p>[tex]z=(x-\mu)/(\sigma)`

where x is the value we are looking for, mu is the mean and sigma is the standard deviation. Using this we have:

[tex]\begin{gathered} P(70Using the properties for distributions and a standard nomal distribution table we have:

[tex]\begin{gathered} P(70Therefore 90.5% (rounded to three decimal places) of the population is on this interval.

b)

We know that unussually high scores in a bell curve are the scores over three standard deviations; then in this case this means scores over 145 points.

c)

In any bell curve 99.73% of the scores are within three standard deviations of the mean.