At a college, the mean GPA of the current body is 2.76 with a standard deviation of .64.?

Question

Please help me compute (two decimal places) the GPA of a student with a z-score of 0.3 and another student with a z-score of -1.4.

Answer 1

z = (sample value - mean)/std dev

0.3 = (sample value - 2.76)/.0.64
z = 2.76 + 0.64*(0.3)

z = 2.952 = rounded to 2.95

z = -1.4 = (sample value - 2.76)/0.64
sample vaue = 2.76 +(-1.4)*0.64 = 1.864 round to 1.86

Answer 2

The z-score associated with an observation x_i of a random variable X is given by

z = (x_i - mean) / standard deviation

Plug in z=0.3, mean = 2.76 and std dev = 0.64, and get

0.3 = (x_i - 2.76) / 0.64
=> 0.3*0.64 = x_i - 2.76
=> x_i = 2.76 + 0.3*0.64
=> x_i = 2.952