1) Entry to a certain University is determined by a national test. The scores on this

Question

test are normally distributed with a mean of 500 and a standard deviation of 100.
Tom wants to be admitted to this university and he knows that he must score
better than at least 70% of the students who took the test. Tom takes the test and
scores 585. Will he be admitted to this university?

^ I already did this question and I got 80.23%

but I need help with the other questions that go with this :

2) For the same test, consider Sarah, whose score is 683. What is her
a) Z score
b) T score
c) Percentile rank
d) What percentage of people scored between Sarah and the mean? How many
people were ahead of her? (Clue: use the Z table).
e) If the mean on the test were 550 and the Sd = 50, what would be Tom and
Sarah’s scores? Would either of them qualify for the University now?

Answer 1

I did not check #1.

2. Z = (score-mean)/SD

Z = (683-500)/100 (calculate)

T = 50 + 10Z

Percentile rank = proportion ≤ score

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores for c, d and e.