Question

Provide an appropriate response.Find Y such that 56.75% of adults have IQ score greater than Y.

129.6

97.5

102.6

110.7

Answer 1

To solve this problem, let us assume the IQ of adults is normally distributed with a mean of 100 and a standard deviation of 15.

Now, let X denote the IQ score of a randomly selected adult.

Thus, P(X > Y) = 56.75% = 0.5675

Corresponding to X = Y, the Z score is (Y - 100)/15

Thus, P{Z > (Y - 100)/15} = 0.5675

From Z table, the above probability of 0.5675 is satisfied for Z > (-0.17)

Thus, (Y - 100)/15 = -0.17

-> Y = 97.5

Thus, the most appropriate response is 97.5