A set of 50 data values has a mean of 21 and a variance of 16. I. Find the standard score (z) for a data value = 31. II. Find the probability of a data value > 31. III. Find the probability of a data value < 31. Show all work. Solution If the variance is 4, sigma is the sqrt(4) = 2 z = (x - mu) / sigma z = (31 - 28) / 2 z = 1.5 So from there, look at a z-table. P(z>1.5) = 1 - .9332 = .0668 P(z<1.5) = .9332.