Question

Sherry missed the lesson on normal distribution and needs to do her homework. Explain to Sherry how to use the mean and standard deviation of a normal distribution to determine the top 7% of the population.
@ganeshie8

Answer 1

pls help??!

Answer 2

Let's see....

Answer 3

We want \[\Phi\left(\frac{x-\mu}{\sigma}\right) = 1-0.07=0.93\]

Answer 4

hmmm. whats the first symbol?

Answer 5

We'd solve for \(x\). Where as \(\mu\) is the man, and \(\sigma\) is standard deviation.

Answer 6

Hmm, well it finds cumulative distribution.

Answer 7

\(x\) would tell us the score that is at the boundary between the 93% and the 7%.

Answer 8

and then what will we do?

Answer 9

Actually "determine the top 7% of the population" is sort of vague. I interpreted it to mean the score at which you would be at the border. The question is not very precise.

Answer 10

eh i know but this is how it is word for word and its worth ten points

Answer 11

First, you use \[ z=\frac{x-\mu}{\sigma} \] to find the \(z\) score. \(\mu\) is mean and \(\sigma\) is standard deviation.
Next, you would look up \(z\) in your \(z\) table.\[
P = \Phi(z)
\]In this case \(P\) is what you find in the table, and it is the probability that your score is under \(x\).

Answer 12

With the current question, we have \(P\) is already provided. When looking at the top 7%, this is the opposite of being in the bottom 93%. So we let \(P = 0.93\).

We do the \(z\) table look up, but instead of looking up \(z\), we find look to see what \(z\) value will give us \(0.93\).

Answer 13

then we can finally solve for \(x\).

Answer 14

so what do i plug in for x in the z score formula

Answer 15

We are trying to find \(x\).

Answer 16

im confused so thats the answer?

Answer 17

Okay, first of all, do you have a \(z\) table with you?

Answer 18

yess

Answer 19

Tell me what it says when \(z=0\).

Answer 20

.5000

Answer 21

How, try to find a \(z\) that will result you in getting \(0.97\)

Answer 22

I mean \(0.9300\)

Answer 23

ok hold on

Answer 24

I cant find that sorry

Answer 25

https://figures.boundless.com/18108/full/normal01.jpe
@wio

Answer 26

You will have to use the closest thing.

Answer 27

uhh ok 1.48

Answer 28

So our \(z\) score is \(1.48\). Do you know what the mean and std dev are?

Answer 29

\[
1.48\approx \frac{x-\mu}{\sigma }
\]

Answer 30

then? no i dont, can you expllain were we got our z score from pls?

Answer 31

Well, typically you learn the \(z\) score is just \[
z=\frac{x-\mu}{\sigma }
\]This is just a normal fact. I could show you where it is from, but the truth is that it would probably confuse you more.

Answer 32

no like in the lessoon we learned thattt the only way to get z score is throught the deviation and first score minus the second but howd youu get it without everything because i have to expllain iit too

Answer 33

Well, I'm not sure then. I don't know what you are talking about.

Answer 34

pls :/ if you cant explain, then can you just give me the final answer with compllete sentences

Answer 35

It seems I can't really help out beyond what I have said.

Answer 36

no can you like give me the summary of the answer I wont have you explain it to me plss?

Answer 37

I don't know the answer.

Answer 38

:( do you know anybody that can help me?

Answer 39

@ranga

Answer 40

@eliassaab

Answer 41

@shamil98