Need Help please show work Thanks Below is a summary of test

Need Help, please show work. Thanks!

Below is a summary of test score in two sections. The questions and possible maximum scores are different in these two sections. We notice that Student A4 in Section A and Student B2 in Section B have the same numerical score. a. (5 points) How do these two students stand relative to their own classes according to their z scores? b. (3 points) Which student performed better? Explain your answer based on their z scores.

Solution

We are comparing here two students A4 and B2

BOth numerical scores are 61, 61 the same.

Calculate Mean and variance of A and B.

A Mean 56.29 std dev = 19.09

Hence z score for A =   = 0.0002

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B Mean 57.375 : sigma =23.44

Z score =  = 0.1549

We see that z score for B is higher than A

Hence B2 did better than A4