Question

1. iq scores have a mean of 100 and a standard deviation of 16. albert einstein reportedly had an iq of 160. a. what is the difference between einsteins iq and the mean? b. how many standard deviations is that? c. convert einsteins iq score to a z - score. d. if we consider “usual iq scores to be those that convert z scores between - 2 and 2, is einsteins iq usual or unusual?

Explanation:

Step1: Calculate difference from mean

$160 - 100=60$

Step2: Calculate number of std - devs

$\frac{60}{16}=3.75$

Step3: Convert to z - score

z - score formula is $z=\frac{x-\mu}{\sigma}$, here $x = 160$, $\mu = 100$, $\sigma = 16$, so $z = 3.75$

Step4: Determine if usual

Since $3.75>2$, it's unusual.

Answer:

a. 60
b. 3.75
c. 3.75
d. No