statistics question: using Z scores?

Question

A sample of six students was selected at random and the number of e-mail messages received by each on that morning was solicited. A statistician converted the results to standard scores, five of which are 0, .267, .535, 0, and 0.

a) What is the standard score for the sixth student?

b) If the first two students received 8 and 9 e-mails respectively, how many did the sixth student receive?

I know the equation I'm supposed to use is Z = X -Xbar/ s
but how do I apply it???

Answer 1

Part A:

Let z be the standard score for the sixth student.
{0 + .267 + .535 + 0 + 0 + z)} / 6 = 0
=>0 + .267 + .535 + 0 + 0 + z=0
=>z=-0.802

Part B:

Let "x_bar" be the csample average & "sigma" be the sample standard deviation.

First student:

0 = (8 - mu) / sigma

=> 8 - mu=0
=> mu=8

2nd student:

267 = (9-mu) / sigma

267 = (9 - 8) / sigma

=> sigma = (9-8) / 267=0.003745

For the 6th student:

Let x be the number of email that the 6th student received.

(x - mu) / sigma = -0.802

=> (x - 8) / 0.003745 = -0.802


=> x = (-0.802*0.003745 ) + 8 = 7.997

Therefore the 6th student received about 8 emails!

Answer 2

Part A: The z-scores of the entire group should average out to 0. So to find the 6th score, you;d take
(0 + .267 + .535 + 0 + 0 + z) / 6 = 0.
This means .802 + z = 0, so z = -.802 .

I'm honestly not quite sure how to do Part B without knowing anything about the standard deviation.