This question is based on normal distribution.

Question

In the general population, IQ is normally distributed with a mean 100 and standard deviation 15.

(a) If you select a person at random from the population, what is the probability that their IQ is between 100 and 110?

(b) Determine the IQ for which 5% of the population have an IQ above this value.

(c) If you randomly selected a group of 50 people from the population, what would the expected value of their average IQ be?

Answer 1

x = IQ

z = (x - mean)/standard deviation

a)

P(100 < x < 110) = P( (100-100)/15 < z < (110-100)/15) = P(0 < z < 0.67) = P(z < 0.67) - P(z < 0) = 0.7486 - 0.5 = 0.2486

b) z for 95th percentile is 1.645

1.645 = (x - 100)/15

x = 15*1.645 + 100 = 124.675

c) the expected value of the average IQ would be the population IQ of 100.