Question

Students taking a standardized iq test had a mean score of 100 with a standard deviation of 15. assume that the scores are normally distributed. (adapted from audiblox 3. find the probability that a student had a score higher than 125. is this an unusual event? explain.

Answer 1

The standardized probability of a normally distributed data is given by
P(X < x) = P(z < (x - mean) / standard deviation)
P(X > x) = 1 - P(X < x)
P(X > 125) = 1 - P(X < 125) = 1 - P(z < (125 - 100) / 15) = 1 - P(z < 25/15) = 1 - P(z < 1.667) = 1 - 0.95221 = 0.04779 = 4.8%

Though it cannot be said to be usual, at the same time it is not unusual because 125 is above the first standard deviation of the mean but below the second standard deviation of the mean.