in a sample of n40 scores X 31 corresponds to z150 and X 39

in a sample of n=40 scores, X= 31 corresponds to z=-1.50 and X= 39 corresponds to z= +0.50. the sample mean is M=36. is this true or false

Solution

As

x = m + z*s/sqrt(n)

Then

31 = m + (-1.50)*s/sqrt(n) [1]
39 = m + (0.50)*s/sqrt(n) [2]

Multiplying equation [2] by 3 then adding,

148 = 4m

m = 37

Thus, FALSE. [ANSWER]