Chapter 5, Problem 5.15P

A large university administers entrance exams to all entering students. The test is administered again as an exit exam for all graduates. The test results for one group of students are given in the table.

Freshman Year	Senior Year
$\bar{X}=53$	$\bar{X}=92$
$s=7$	$s=4$

a. The scores for five students on both tests are listed below. For each student, calculate $Z$ scores and determine whether the student performed better as a freshman or as a senior.

Student	Score, Freshman Year	Score, Senior Year
A	57	97
B	51	94
C	45	82
D	73	101
E	62	98

b. Determine the probabilities that randomly selected students will have scores in each of these ranges:

Freshman Year
Score	Probability
Less than 52
Less than 57
Between 40 and 50
More than 51
More than 62

Senior Year
Score	Probability
Less than 88
Less than 98
Between 80 and 100
More than 97
More than 85