Question

iq tests have a mean of 100 and sd of 16. einsteins iq was 160. what is the z - score of his iq?

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values

Here, \(x = 160\), \(\mu=100\), and \(\sigma = 16\). So, \(z=\frac{160 - 100}{16}\).

Step3: Calculate the numerator

\(160-100 = 60\). Then the formula becomes \(z=\frac{60}{16}\).

Step4: Simplify the fraction

\(\frac{60}{16}=\frac{15}{4}=3.75\).

Answer:

\(3.75\)