Need help with Z-Score / SD problems, please help.

dennyyildiz35 said:

"A big test was given by the math department. Forty-three students had z-scores below -1.25. How many students took the test?"

- I understand this problem is asking for the population given the sample size... and I believe the answer is 430 going off of my choices, but how?? Please show how to do it on the calculator and if there is a formula to do it by hand.

"Sam got a score of 80 which he worked out to be 1.25 standard deviations above average. The standard deviation for the entire class was 5. What was the class average?"

- I got really confused on this problem because it is asking what the class average is, yet the problem is literally telling us in the beginning. ( how 80 is 1.25 SD above average... Wouldn't the average then be 78.75... NO )
- EDIT: For this problem there was no answer choice of 78.75, but 73.75, 86.25, 81.25, 85, and 75. ( I believe the most logical answer here would be 73.75... but how??)

Click to expand...

SD = 5

Average= 80 - 5 * 1.25 = ???

Have you been taught - how to read z-distribution chart? and the "meaning" of it?

dennyyildiz35 said:

"A big test was given by the math department. Forty-three students had z-scores below -1.25. How many students took the test?"

- I understand this problem is asking for the population given the sample size... and I believe the answer is 430 going off of my choices, but how?? Please show how to do it on the calculator and if there is a formula to do it by hand.

Click to expand...

Suppose that below z=-1.25 corresponds to 20%. So 20% of the students is 43. You should know how to go from 20% =43 students to how many students there are. Of course you need to find the correct % first for below z=-1.25.

Are you understanding any of this material from class?
Jomo

dennyyildiz35 said:

"Sam got a score of 80 which he worked out to be 1.25 standard deviations above average. The standard deviation for the entire class was 5. What was the class average?"

- I got really confused on this problem because it is asking what the class average is, yet the problem is literally telling us in the beginning. ( how 80 is 1.25 SD above average... Wouldn't the average then be 78.75...)

Click to expand...

I think first that you need to know what it means to say that the standard deviation for the entire class is 5. Once you understand the answer to my question the answer should be immediate.
Jomo

Subhotosh Khan said:

SD = 5

Average= 80 - 5 * 1.25 = ???

Have you been taught - how to read z-distribution chart? and the "meaning" of it?

Click to expand...

For the equation above, the answer is equal to 93.75, but in my choices there are only: 73.75, 86.25, 81.25, 85, and 75.
And for the chart, I want to know how to do this problem without any charts as I have a midterm final soon and I would like to know how to work it out with a calculator or by hand.

Jomo said:

Suppose that below z=-1.25 corresponds to 20%. So 20% of the students is 43. You should know how to go from 20% =43 students to how many students there are. Of course you need to find the correct % first for below z=-1.25.

Are you understanding any of this material from class?
Jomo

Click to expand...

To find the correct % for below z=-1.25, won't I need the mean and SD? I don't have either of those information. If I did, I would use normalcfd() if I'm not wrong, to find the below %.

To expand slightly on the post by Subhotosh Khan, let t be the test score, u equal the average, s the standard deviation, and z the number of standard deviations, then
z = (t - u) / s
So if you have the number of standard deviations, the test score, and the standard deviation
u = t - s * z
BTW: I very strongly suggest you redo your calculations if you got 93.75 as the answer.


As far as how many students took the test, at least one assumption needs to be made and that is the test score distribution. The 'z-scores' seems to indicate that the distribution was Normal but, still, that is not a positive thing. Once the Normal distribution is assumed, if, as asked above, you know how to read z-distribution chart and the "meaning" of it, the answer is a matter of looking up the answer as pointed out by Jomo.