Answer:
21.94% of people aged 20 to 34 have IQs between 125 and 150.
Step-by-step explanation:
<u>The complete question is:</u> Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with μ = 110 and σ = 25.
What percent of people aged 20 to 34 have IQs between 125 and 150?
Let X = <u><em>Scores on the standard IQ test for the 20 to 34 age group</em></u>
SO, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 110
= standard deviation = 25
Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X 125)
P(X < 150) = P( <
) = P(Z < 1.60) = 0.9452
P(X 125) = P(
) = P(Z
0.60) = 0.7258
The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.
Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%