Comparing Test Scores SAT scores have a mean of 1518 and a s

Comparing Test Scores SAT scores have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which is relatively better: a score of 1030 on the SAT test or a score of 14.0 on the ACT test? Why?

Solution

x = 1500 z = (1500 - 1518) / 325 = -0.055384615 P(X < 1500) = P(Z < -0.055384615) = 0.4761 = 47.61% ote that I rounded z to -0.06, which gave probability of 0.4761 If I had rounded to -0.05 instead, I would get 0.4801 In reality, actual probability is somewhere in between. ------------------------------ Let Xbar be sample average. Then Xbar is normally distributed with mean = µ = 1518 standard deviation = s /v(n) = 325 /v(100) = 32.5 P(Xbar < 1500) = P((Xbar-µ)/s.d. < (1500-1518)/32.5) = P(Z < -0.553846154) = 0.2912 (check table above) = 29.12%