Question

IQ scores are normally distributed with an average score of 100 and a standard deviation of 15. a.) People with an of at least 122 are considered above average in intelligence. What z-score corresponds to an IQ of 122? SHOW YOUR WORK ON PAPER. Round to 1 decimal place b.) Using the table above and your answer to part a, what percent of the population would have an IQ of 122 or higher? c.) Einstein was said to have an IQ of 160. What would this mean? SHOW YOUR WORK ON PAPER. Explain your answer mathematically ! d.) Your neighbor told you they recently took an IQ test and scored in the 58th percentile but they can't remember what their IQ is. What is their IQ? SHOW YOUR WORK ON PAPER e.) Fill in the values for the normal distribution curve that represents the values within 3 standard deviation from the mean. Be sure to label the mean and the value corresponding to each standard deviation.

Answer 1

We have to use the z-score formula

`\begin{gathered} z=(x-\mu)/(SD) \\ \\ z=(122-100)/(15)=(22)/(15)=1.47 \end{gathered}`

A z-score of 1.5 approximately has an IQ of 122 and above.

b) Let's see the z-table

0.9332 is the corresponding value, so the percent is 1 - 0.9332 = 0.0668 x 100% = 6.68%

c)

`z=(x-u)/(sd)=(160-100)/(15)=(60)/(15)=4`

The corresponding value is 0.9997. This means that Einstein has an IQ greater than 99.997% of the population

d) He scored 58th percentile, which is a z-score of 0.2.

So his IQ is:

`\begin{gathered} 0.2=(x-100)/(15) \\ 15(0.2)=x\text{ - 100} \\ 3+100=x \\ x=103 \end{gathered}`

His IQ was 103.

e)

So the values between 3 standard deviatiosn are 100 - 15(3)= 100-45 = 55

100 + 15(3) = 100 +45 = 145.

The values between 3 SD are the ones between 55-145