Need Help With Z Scores (2 Questions).

[Blonk]

I have 2 questions that I have no idea how to figure out because I didnt pay attention in class.

1. A student's standard mark on a class test is z= -2.1.
    On the basis of this score, and assuming the test marks follow a normal distribution, it can be concluded that his test mark
    was:
A: in the bottom 2.5% of marks in the class.
B: in the bottom 5% of marks in the class.
C: in the bottom 16% of marks in the class.
D: in the top 5% of marks in the class.
E: in the top 2.5% of marks in the class.

2. A student's standardised mark on a class test was z= -1.7. The mean mark for the class is 55 and the standard deviation is
    2.85.
    Their mark on the test was closest to:
A: 49
B: 50
C: 53
D: 58
E: 60

If anyone is able to give me the answers for these 2 questions and provide some form of working out or how to work it out on the ClassPad calculator, please help me out!

[FatnessFirst]

z score indicates how many standard deviation it is from the mean in that case it is 2 (2.1) standard deviation. since it's negative it means it's below the mean so bottom 2.5%

[Wezanator123]

for Q2) use algebra for the formula to work out z-score:

so: z-score = x-value - Mean
                 ------------------------
                        S.d

Sub the z-score, mean and s.d

so

-1.7 = x - 55
          ---------
              2.85

then:  2.85 x -1.7 = x - 55

after you find 2.85 x -1.7 add 55 to it and u should get your answer

[Wezanator123]

woops i mean the student's mark

[Blonk]

z score indicates how many standard deviation it is from the mean in that case it is 2 (2.1) standard deviation. since it's negative it means it's below the mean so bottom 2.5%

I dont really get that :/ I get that its 2 Standard Deviation from the mean and thats its a negative so its in the bottom of the class but then how did you just get to 2.5%?
Does that mean if the z score is -5.1 then its in the bottom 5% of the class? And if the z score is -16.3 or something then its in the bottom 16% of the class?

[Keo]

z score indicates how many standard deviation it is from the mean in that case it is 2 (2.1) standard deviation. since it's negative it means it's below the mean so bottom 2.5%

I dont really get that :/ I get that its 2 Standard Deviation from the mean and thats its a negative so its in the bottom of the class but then how did you just get to 2.5%?
Does that mean if the z score is -5.1 then its in the bottom 5% of the class? And if the z score is -16.3 or something then its in the bottom 16% of the class?

No, for further maths theres only 3 SD, 1SD= 68%, 2SD= 95%, 3SD= 99.7%

it doesnt stretch beyond 4 in this math

[Blonk]

No, for further maths theres only 3 SD, 1SD= 68%, 2SD= 95%, 3SD= 99.7%

it doesnt stretch beyond 4 in this math

Haha yeah I know the 68/95/99.7 rule but I dont know how he got from being 2SD to bottom 2.5% of the class. To me its like theres a massive step missing. . . .

[Blonk]

DONT WORRY I GOT IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! YAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYA!

[onur369]

-1.7 x 2.85 + 55 = 50.155 ?

[Keo]

DONT WORRY I GOT IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! YAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYAYA!