Question

The probabilities that a batch of 4 printers will contain 0, 1, 2, 3, and 4 defective printers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the standard deviation for the probability distribution.

Answer 1

s = 1.05
s = 0.77
s = 0.71
s = 0.59

Answer 2

@amistre64

Answer 3

hmm, what we are dealing with in this case is not a normal distribution so there is a different approach to it

Answer 4

do you recall doing something other than a normal distribution in your course?

Answer 5

This is the first time i've ever taken this course :/

Answer 6

well, we want to determine the mean. i know how, but i need to see what your thoughts are to start with.

Answer 7

There is a problem that deals with I think a more "simple" version of standard devation, but I don't get most of it . x_x

Answer 8

Well I tried adding them all up then dividing by 5. I got a really weird decimal number.

Answer 9

yeah, thats not gonna work here since you dont actually have 5 points to play with, but more

Answer 10

More?

Answer 11

yep, you are given x, and the number of times it occurs in say 1000 parts

Answer 12

Yeah I am unsure of what to do :/

Answer 13

recall that the probability of something happening is calculated as:

# times it occurs
--------------
# of total events

0 happens: 4521 times out of 10,000 tries
1 happens: 3970 times out of 10,000 tries
2 happens: 1307 times out of 10,000 tries
3 happens: 0191 times out of 10,000 tries
4 happens: 0010 times out of 10,000 tries

Answer 14

there is a formula for variance of a probability distribution
first find the mean, E(X).
the Var = E(x^2) - E(x)^2

Answer 15

essentially:

mean = sum of (x*p(x))

Answer 16

yes jayz, that is what i was heading towards

Answer 17

Idk. I am still confused, sorry :/.

Answer 18

Judach i can send you an excel, its difficult to draw a table here

Answer 19

I'm on a computer at school. I doubt i'd be able to receive it.

Answer 20

the expected value of x, noted as E(X), is the mean of the set.

\[E(X)=\sum x~p(x)\]
x p(x) x*p(x)
0 .4521 0
1 .3970 .3970
2 .1307 .2614
3 .0191 .0573
4 .0010 .0040
add these up

Answer 21

Just the right column or all of them?

Answer 22

nice work @amistre64

Answer 23

yes, we need to know the sum of the last column

if you cant recall the 'shortcut' formula: then we can always do:

VAR(X) = sum (x-E(X))^2

Answer 24

.7197 for the right column

Answer 25

.3970
.2614
.0573
.0040
------
.7197

seems right to me

Answer 26

Then what? x_x

Answer 27

then we can use the process of subtracting the mean from the data points and working the process :) it simpler to do by say a ti83 or excel of you have one of them

Answer 28

I have a calculator available.

Answer 29

A TI-83

Answer 30

ti83 is good, do you know how to make a list?

Answer 31

No ;/

Answer 32

I know it's 2nd or Alpha, then something else.

Answer 33

Stat -> 1:Edit

Answer 34

you have a list button i believe. takes you to the lists directly. or that option may do fine

Answer 35

I'm at a screen that asks for type and says Xlist, Ylist under it, but I don't have a way to edit.

Answer 36

Nvm
I have it,

Answer 37

What do I put in L1?

Answer 38

under L1, enter in your 0,1,2,3,4

under L2 put in their decimal probabilities that they give you

Answer 39

I have 45 mins and 5 more problems ;/

Answer 40

then the ti83 is your best friend if you know how to use it :)

Answer 41

My 0,1,2,3,4? You mean the numbers I added up to get .7197?

Answer 42

L1 L2
0 .4521
1 .3970
2 .1307
3 .0191
4 .0010

Answer 43

done

Answer 44

exit out to the main screen and go to your distribution menu:

so: quit, and then 2nd,VARS

Answer 45

Ok

Answer 46

choose the 1-var stats in the distribution menu and enter L1,L2

(2nd 1 , 2nd 2) then hit enter
^
thats the comma key

Answer 47

the button right above the '7' is a list seperater that allows you to input more than one list is all

Answer 48

1-var? you mean the normpdf?

Answer 49

no. it may be under stats. been awhile :)

Answer 50

I have DISTR and DRAW

Answer 51

stats, test

Answer 52

Don't have a 1-var in there either.

Answer 53

stat, calc, 1-var

Answer 54

Yeah found it.

Answer 55

s=1.5

Answer 56

i cant verify that from a ti83, my batteries been dead for ages now. but yeah, that should work the process.

Answer 57

Alright thank you. :/ Sorry for how long this took. I am not fully clear on stand deviation even now, but thank you .

Answer 58

computing it takes time to learn is all. and time is something you say you havent got at the moment. in my stats1 class the teacher had us use the ti83 for simplicities sake

Answer 59

Yeah I don't have a teacher for this course. I have to "self teach" myself.

Answer 60

Gonna close this one and open up a different question. Thank you again.

Answer 61

good luck :)