IQ scores are distributed normally with mean 100 and standard deviation 15. (IQ

Question

IQ scores are distributed normally with mean 100 and standard deviation 15. (IQ scores are actually measured discretely, it's impossible to get an IQ of 91.5 for example. For this problem assume that they are measured continuously.) a) According to the Wechsler IQ classification, an IQ between 90 and 110 is considered average. Find the percentage of the population which has an average IQ. b) An IQ scores between 110 and 120 is considered "high average". Find the percentage of the population with a "high average" IQ.

Explanation / Answer

Both params of the normal distribution are given below:

Mean =100

Stdev = 15

We will use them to standardize the RV.

We will also use the Z tables to solve the problem

a. P(90<X<110) = P(90-100/15<Z<110-100/15) = P(-.66<Z<.66) = 2*(.7454-.5) = .4908

49.08% of people get a score between 90 and 110

b. P(110<X<120) = P(110-100/15<Z<120-100/15) = P(.66<Z<1.33) = 0.9082- 0.7454 = .1628

So, 16.28% of them get "high average"

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