Question

I need help understanding the formula to calculate: If the top 10% of students are given A's, what is the lowest mark a student can get and still receive an A. Normal distribution, mean = 62 sd = 11. I can do the calculations but don't know how to set this up correctly. Thanks

Answer 1

call in the big guns... @jim_thompson5910
please help me @Jhannybean ...?

Answer 2

All the J people,eh?

Answer 3

Ew, standard deviation.

Answer 4

no, just u 2 because ur special ;P

Answer 5

the instructor always uses something like P ( x < ----) P (Z < ----) or P (x > ---) P ( z > ____). Something to this effect...I don't know what way I am going, to the left, or right.

Answer 6

right, the top 10 %

Answer 7

you want to find the value of k such that

P(X > k) = 0.10

Answer 8

My instructor has never used that formula...

Answer 9

alternatively, you want to find the value of z such that

P(Z > z) = 0.10

using mean = 0 and standard deviation = 1

once you get the critical value z, you would convert it to a raw score

Answer 10

If I want the top 10%, do I need to find the z for 90th percentile and subtract from one?

Answer 11

no just the z value for the 90th percentile

Answer 12

the 90th percentile is the value that is above 90% of the distribution

Answer 13

z for 90th percentile is 1.28

Answer 14

ex: sometimes your grade or report card will say "you are in the 90th percentile", which would mean that your grade is higher than 90% of the student body

Answer 15

that is correct

Answer 16

ie P(Z > 1.28) = 0.10 roughly

Answer 17

now convert z = 1.28 to a raw score

Answer 18

if you're not sure how to convert, then you just solve for x

z = (x - mu)/sigma

1.28 = (x - 62)/11

Answer 19

that is a similar formula he has had us use...this is what I came up with...1.28 (11) + 62 = 76.08 as the lowest possible score to achieve an A...but that doesn't sound reasonable

Answer 20

76.08 is the correct answer

Answer 21

btw, if you solve for x, you get

1.28 = (x - 62)/11

1.28*11 = x - 62

1.28*11 + 62= x

x = 1.28*11 + 62

Answer 22

which is what you did

Answer 23

ok...thanks...you guys online write your formulas differently than he shows us in class...I am so confused..

Answer 24

quick query, what'd u use to get the sd value as 1.28 for 90%...?

Answer 25

No...since I need to find my x value...I look for the 90th% ...the z value for .9000 = 1.28. then I solve for x by using 1.28 (11) + 62 ...(62 is mean) and 11 is sd...

Answer 26

yeah, but is there an equation to work out each of the percentiles?
or is it a table you read off?

Answer 27

sorry...I am NOT a math person and have no idea what I am doing....Yes, we have a Z table in our stats book...
in fact...I am wondering if I'll get thru this class with a passing grade...when we are In class and do problems together, I get it...but later, it looks foreign...and I have so many pages of notes that I can't find what I'm looking for when I need it...

Answer 28

all good then, cheers beal and good luck
thanks again for coming jim and Jhanny

Answer 29

the formula you're using to convert is

x = z*mu + sigma

and that's just a rearranged version of what I originally wrote

Answer 30

... u sure it's not

z* sigma + mu = x

i had a look at the original above...

Answer 31

oh sry, had them mixed up, yes it's x = z*sigma + mu

Answer 32

ah, cool

Answer 33

Did I do it wrong then? He provided 2 formula's depending on what I need to find....Z = (x-mu)/sigma or X = mu + Z (sigma) ....but I still don't know how to set the problem up so I know what direction to go P ( X < or > of some number) = P (Z < or > of some number)....How can I know this and keep it straight?

Answer 34

well you have a z chart, so use P(Z< ...) or P(Z >....)

Answer 35

you want the top 10%, which means you want to find the value that will replace the question marks

P(Z > ???) = 0.10

Answer 36

So, although I want the top 10%, (Z > ??) I look at the 90th % to the left of Z. And if I wanted the least of some number, I would set it up as P (X < ?) P ( Z < ?)...right?

Answer 37

yeah if you want the bottom 90%, then you want to find some number that replaces the question marks

P(Z < ???) = 0.90