Question

I need someone to walk me through how to do this, I do not want the answer I just need help understanding it better. (statistics)

A set of 50 data values has a mean of 45 and a variance of 9.
I. Find the standard score (z) for a data value =52.
II. Find the probability of a data value <52.

Answer 1

ok will help u
first tell me what is mean?

Answer 2

and what type of distribution are we looking at?

Answer 3

This is for Statistics class. there is not many people online well there is no one online for Statistics

Answer 4

i m here tell me what is mean

Answer 5

it this was a normal distribution; with a mean of 0 and an sd pf 1; it would be a piece of cake :)

Answer 6

given a ztable and such

Answer 7

yeah amistre u r right

Answer 8

what is a sd pf?
yeah I have the tables, but need to work it out.

Answer 9

(off the subject, is open study compatible with FireFox?) I ask because mine is not loading your responses.

Answer 10

the formula for standard score is
z= x-(mean of x) /standard deviation of x

Answer 11

"what is a sd pf?"

a typo .... an sd of 1. sd is of course short for standard deviation

Answer 12

to understand what is happening you have to notice that we shift the given distribution into a standard normal distribution so that we can work with it easier

Answer 13

ok yeah. I got you

Answer 14

ok

Answer 15

since the mean of this is at 45; and all its associated points stem from it; we need to subtract it all by 45 to get the mean to hover over "0" .. right?

Answer 16

why hover over "0"?

Answer 17

because the ztables have been constructed for a mean of 0 and an sd of 1

Answer 18

oh ok I am with you now.

Answer 19

the integral for the distribution curve is easiest to determine from a mean of 0 and an sd of 1

Answer 20

so; we take out distribution and subtract the mean from it; but our sd needs to be adjusted as well; the sd is simply the sqrt(var)

var = 9, so sd = sqrt(9) = 3 in this case

Answer 21

we need to divide the sd by some number to get it to equal 1;

Answer 22

well, sd/sd = 1

Answer 23

this is where the z formula comes from:

\[z=\frac{x-mean}{sd}\]

Answer 24

and once we know the "z" score; we can evaluate it with a z table

Answer 25

so the z score of 52 in this case is:

\[z=\frac{52-mean}{sd}\]
\[z=\frac{52-45}{3}=\frac{7}{3},or\ 2.3333\]

Answer 26

I am with you.

Answer 27

the rest is just reading the information given by a ztable and those differ depending on who the author of the material is

Answer 28

some measure the Pvalue of z from the mean, some from the left tail, some from the right, and others with any mix in betwenn

Answer 29

ok, let me look it up.

Answer 30

look for the left of the table to be 2.3, and connect that to the top of the table .03

Answer 31

0.4901

Answer 32

.......................03
. .
. .
. .
. .
2.3------->(Pvalue)

Answer 33

so how do I write the answer to that, do I just put z=0.4901?

Answer 34

no, the z score, or z value is just 2.33; we use that for the next part tho

Answer 35

since that value is less than .5; and i know the zscore is to the right of the mean; that looks to be a measure of the area FROM the mean to the z

Answer 36

so what is the answer to the first one? How do i write it out.

Answer 37

Find the standard score (z) for a data value =52. z = 2.33

Answer 38

OK on the the next one?

Answer 39

the next one takes some work:

Find the probability of a data value <52



in this case the total area to the left of 52 is the addition of .5 and your z-scores value