Question

scores on the wechsler adult intelligence scale (an iq test) for the 20 - to 34 - year - old age group are approximately normally distributed with $\mu = 110$ and $\sigma = 25$.
mensa is an elite organization that admits as members people who score in the top 2% on iq tests. what score on the wechsler adult intelligence scale would an individual aged 20 to 34 have to earn to qualify for mensa membership?
134.5
185
58.75
161.3

Explanation:

Step1: Find the z - score

Since we want the top 2%, the area to the left of the z - score is \(1 - 0.02=0.98\). Using a standard normal table or calculator, the z - score \(z\) corresponding to an area of \(0.98\) is approximately \(z = 2.05\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\). We know \(\mu = 110\), \(\sigma = 25\), and \(z = 2.05\). Rearranging the formula for \(x\) gives \(x=\mu+z\sigma\).
Substitute the values: \(x = 110+2.05\times25\).
First, calculate \(2.05\times25 = 51.25\).
Then, \(x=110 + 51.25=161.25\approx161.3\).

Answer:

161.3