for a population with a standard deviation of o 12 a score

for a population with a standard deviation of o = 12, a score of X = 44 corresponds to z = -0.50. what is the populationr mean?

Solution

z = (x-m)/s x = raw score = 44 m = mean = unknown s = std deviation = 8 z = z score = -0.5 -0.5 = (44 - m)/8 <--you have to solve algebraically, so move the 8 to the other side (-0.5)(8) = 44 - m <--you have to move the 44 to the other side to isolate m (-0.5)(8)-44 = -m <--you have to solve for positive m, so multiply both sides by -1 -1[(-0.5)(8)-44] = m 48 = m To double check your answer, plug in the #s and see if you get the same z-score: (44 - 48)/8 = -0.5