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 $sigma = 25$.
what percentage of people aged 20 to 34 have iqs between 125 and 150?
94.52%
21.95%
78.05%
27.43%

Explanation:

Step1: Calculate z - scores

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\).
For \(x = 125\), \(z_1=\frac{125 - 110}{25}=\frac{15}{25}=0.6\).
For \(x = 150\), \(z_2=\frac{150 - 110}{25}=\frac{40}{25}=1.6\).

Step2: Use the standard normal distribution table

We know that \(P(Z<z_1)=P(Z < 0.6)\) and \(P(Z<z_2)=P(Z < 1.6)\).
From the standard - normal table, \(P(Z < 0.6)=0.7257\) and \(P(Z < 1.6)=0.9452\).

Step3: Calculate the probability

The probability \(P(0.6<Z<1.6)=P(Z < 1.6)-P(Z < 0.6)\).
\(P(0.6 < Z < 1.6)=0.9452-0.7257 = 0.2195\).

Answer:

21.95%