Question

check my work! will medal

Answer 1

2.

Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g. If 280 different quarters are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.550 g and 5.790g?

A.

0.9998
B.

0.0524
C.

0.0002
D.

0.9476

Answer 2

i got D, well it was closest to D

Answer 3

@ganeshie8

Answer 4

i got 0.9464 so i assumed it was D

Answer 5

I used the central limit theorem

Answer 6

yes, that is correct.

Answer 7

positive? i thought i had to do something with 280 but i dont remeber, lol sorry im 10 lessons behind and my teacher wont help me understand how to work it out lol

Answer 8

@Brekitty01

Answer 9

if the site works ... we migh tbe able to do this

Answer 10

ok

Answer 11

you have a modified standard deviation which they call a standard error (SE)

SE = sd/sqrt(n) were n is the sample size

Answer 12

if you take your original zscore for the end point and multiply them by sqrt(n) its should adjust them as needed

Answer 13

ok hmmm, so 280 is the sample size?

Answer 14

yep

Answer 15

so i have to divide 0.062 by the sqrt of 280?

Answer 16

it has something to do with a point estimator ... the standard error is the point estimator for the standard deviation of the population

and yes

Answer 17

it has to do with the standard error of the mean

Answer 18

sorry lol my teacher kinda left my brain a bit blank give me a sec, am i literally finding the sqrt of 280? or just simply dividing 0.062 from 280

Answer 19

recall that\[z=\frac{x-\bar x}{\sigma}\]
when the data set are sample means, the standard deviation (sigma) is a modification of this
\[z\sqrt n=\frac{x-\bar x}{\sigma/\sqrt n}\]

Answer 20

oh ok that is the part where i got lost lol

Answer 21

so z= 5.550-5.670/0.062 sqrt. 280

Answer 22

Currently, quarters have weights that are normally distributed with
a mean of 5.670 g and
a standard deviation of 0.062 g.

If 280 different quarters are inserted into the vending machine
, what is the probability that the mean
(of this sample of quarters)

falls between the limits of 5.550 g and 5.790g?

z1 = 5.55 - 5.67 z2 = 5.79 - 5.67
---------- ---------
.062 .062

this is what you would usually want to do, but since we are dealing with a sample of means, there is a adjustment according to the sample size we are playing with. z is adjust by sqrt(n)

Answer 23

yes i have that except i used the large numbers like 5.550 and 5.670

Answer 24

fro both of those i got 0.0268 and 0.9732 then subtracted and got 0.9464

Answer 25

you used left tails so subtracting them gives us the middle of it all, good

Answer 26

ok so what now?

Answer 27

then that would be the probability between the deisred endpoints

Answer 28

oh so that is the answer to the problem?

Answer 29

because then it would still be a standard error

Answer 30

im reading to make sure im thinking correctly

Answer 31

its cool :)

Answer 32

ive been stuck on this lesson fro 3 weeks and my teacher wont help me >->

Answer 33

spose we took a large number of samples of size n

sample1 has a mean of m1 and a deviation of sd1
sample2 has a mean of m2 and a deviation of sd2
sample3 ... mean of m3 ... sd of sd3
etc

the means of the samples, by the central limit thrm, are normally distributed and have a standard deviation of the means (the standard error of the means)

Answer 34

the central limit thrm says the the mean of the sample means approaches the population mean for a large number of samples;

Answer 35

ok

Answer 36

the wording is often the hardest thing to determine... it may be that the 280 is given to show a large enough sample size and we do a usual zscore.

Answer 37

so do i do the sqrt formula twice with z1 and z2 to find the correct answer?

Answer 38

like since its not 0.9464 than i obviously have to plug in the sample size which would be 280

Answer 39

i think

Answer 40

well, since 1 is not an option ... lets try it without the sqrt(280)

http://www.wolframalpha.com/input/?i=P%28%285.55+-+5.67%29%2F.062%3Cz%3C%285.79+-+5.67%29%2F.062%29

Answer 41

.9471 is what the wolf tell us; so depending on how accurate your calculations are and the tables you want to use ...

Answer 42

so what do you think, D?

Answer 43

because both of our answers are close but not exact

Answer 44

yeah, D works for me, but i cant say if its 'correct' of not. but it is what i would pick

Answer 45

ok thanks ill let you know

Answer 46

if i need any more help ill just message you. THANKS

Answer 47

it was incorrect, oh well.

Answer 48

tag, or send a link yeah. but the way the site is at the moment its just broken

Answer 49

does it tell the correct one? maybe A?

Answer 50

no it just say incorrect and makes me move to the next question. oh well lol

Answer 51

.... bummer, wish there was a mathlab practice problem that could be similar

Answer 52

do you know any websites where they would solve the problem for me and explain the solutions?

Answer 53

do you have a textbook that you are using by chance?

Answer 54

no, my teacher has us using something called gradpoint, its the whole lesson and then a 10 question quiz thing at the end

Answer 55

http://interactmath.com/PlayerPractice.aspx?bookId=91428&chapterId=7&sectionId=5&exerciseId=1&type=3

Answer 56

inteactmath.com is a good practice site, you press enter, pick a book related to your topic, and work problems that have explanations if you need them

Answer 57

question 2 of the link feels like your problem