Problema Solution
In a set of ACT scores where the mean is 25 and the standard deviation is 3.32, how many scores are lower than 21.68? How many of the 100 scores are expected to be below 31.64?
Answer provided by our tutors
We will assume that we have a normal distribution
Number of scores to be less than 21.68 (out of 100) is:
100 * P(X < 21.68) = 100* P(Z < (21.68 - 25)/3.32) = 100*P(Z < -1) = 100*(0.1587) = 15.87 or approximately 16 scores.
Number of scores to be bellow than 31.64 (out of 100) is:
100 * P(X < 31.64) = 100* P(Z < (31.64 - 25)/3.32) = 100*P(Z < 2) = 100*(0.9772) = 97.72 or approximately 98 scores.