IQs are normally distributed with a mean of 100 and a standa

IQ\'s are normally distributed with a mean of 100 and a standard deviation of 15.

a. if a person is chosen at random, what is the chance that he or she will have a score over 115.

Two persons are chosen at random.

b. What is the chance that both will have a score over 115.

c. What is the chance that at least one will have a score over 115?

Solution

X be the score

X~ N(100,15)

P(X > 115) = 0.1587 Excel function used is 1 - normdist(115,100,15,1)

Y be the number of persons whose score is > 115 is chosen

Y ~ B(0.1587,2)

P(Y=2) = binomdist(2,2,0.1587,0) = 0.0252

P(Y>=1) = 1 - P(Y=0) = 1-binomdist(0,2,0.1587,0) = 0.7078