suppose certain coins have weights that are normally distributed with a mean of 5.767 g and a standard deviation of 0.076 g. A vending machine is configured to accept those coins with weights between 5.677 g. and 5.857 g
a. If 290 different coins are inserted into the vending machine, what is the expected number of rejected coins? (round to the nearest integer

- anonymous

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- mathmale

Melissa, I tried to help you, but left when I received no response from you for 15-20 minutes. Can you go back to your original posting of this question?

- anonymous

I was trying to find the z score

- anonymous

I am slow :(

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## More answers

- anonymous

I found the

- mathmale

yes? found the z-score? Please share y our work.

- anonymous

yes

- anonymous

5.857 - 5.767/0.076 = 0.09/0.076= 1.2

- anonymous

right?

- anonymous

then 5.677 - 5.767 / 0.076 = 0.09/0.076 = -1.2

- anonymous

so my z scores would be 1.2 and -1.2

- mathmale

At first glance it appears to be correct. So, 5.857 grams is 1.2 standard deviations above the mean.
Use a table of z scores to find the AREA under the nomal curve to the left of z=1.2.
Then, do the same for the left boundary: find the AREA under the normal curve to the left of z=-1.2. Subtract the smaller area from the larger. The

- mathmale

result is the area under the normal curve between z=-1.2 and z=1.2.

- anonymous

give me a second. I am very new at this. Going to do my best

- anonymous

having a hard time :(

- anonymous

Which column of numbers do I look at?

- anonymous

I have found 1.2 and -1.2 but then I do not know what to look for after that?

- mathmale

Have you found the AREA to the left of z=1.2? If so, what is that area?
What is the AREA to the left of z=-1.2?

- anonymous

do you want me to look on the z score table?

- mathmale

Yes. Do you have a z-score table in front of y ou?
If not, look at this one:
https://www.google.com/search?q=table+of+z+scores&espv=2&tbm=isch&imgil=jqtSneBuWDdlbM%253A%253BA_vCxSVFbVWILM%253Bhttp%25253A%25252F%25252Fcosstatistics.pbworks.com%25252Fw%25252Fpage%25252F27425647%25252FLesson%25252525200311&source=iu&pf=m&fir=jqtSneBuWDdlbM%253A%252CA_vCxSVFbVWILM%252C_&biw=1360&bih=673&usg=__3DTZCKl9SIeRTcEe_T8ubTfW5LE%3D&ved=0ahUKEwifl_it5tbJAhUL9mMKHWnaDYQQyjcILA&ei=BFNsVp-FGYvsjwPptLegCA#imgrc=jqtSneBuWDdlbM%3A&usg=__3DTZCKl9SIeRTcEe_T8ubTfW5LE%3D

- anonymous

If so, I do not know what to look at. I am having a hard time using the chart.

- mathmale

You are to find 1.2 in the "z" column. Are you comfortable doing that?

- anonymous

I found 1.2

- anonymous

now what do I look for?

- mathmale

good. immediately to the right of the z column is a column marked 0.00. start at the top of this column and move downward to the entry next to z=1.2. What decimal fraction do you see there? Type that in here.

- anonymous

0.8849

- mathmale

beautiful.

- mathmale

That's the area to the left of z=1.2

- anonymous

0.0985

- anonymous

that was for -1.2

- mathmale

Great. Now subtract the smaller area from the larger area.

- anonymous

0.7864?

- mathmale

right. very, very good. That fraction represents the fraction of the total number of coins whose weights are within -1.2 and 1.2 standard deviations .

- anonymous

So is that my answer?

- anonymous

78 coins?

- anonymous

or would it be 79 coins?

- mathmale

The experimenter takes a sample of 290 coins. To find the expected number of coins that are between the two given coin weights, multiply 290 by 0.7699 and round off your answer to the nearest whole number. Is that how you got 78 / 79?

- anonymous

how did you get 0.7699?

- anonymous

I got 0.7864

- mathmale

Right. I got my .7699 on my calculator. There's an arithmetic error somewhere.
The important thing is that you know where this fraction comes from and what it means.

- mathmale

Try again: Look up z=-1.2 and copy down the fraction immediately next to it.

- anonymous

0.8849

- anonymous

0.0985

- anonymous

so I would take 0.8849 - 0.0985 = 0.7864

- mathmale

That seems to be where the error is; I get as area to the left of z=-1.2 the fraction 0.1151, whereas you've obtained 0.0985.

- anonymous

then take hmm wonder why?

- anonymous

let me look again

- mathmale

Wish I could see the z-score table you're using. I don't have one in front of me; my areas come from a table found on the Internet.

- anonymous

â€“1.2 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151

- anonymous

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

- mathmale

Without actually seeing your z table, I can't do much problem shooting.
You found z=-1.2 in your table, and then from the column immediately next to it, found 0.0985, whereas I find 0.1151.

- anonymous

yes. Should I use a different table?

- mathmale

Everything else we've done up to here has been fine.
Have you a friend or fellow student with whom you could discuss this discrepancy?

- mathmale

It'd be worth looking for a different table, yes. The table you use MUST show negative z scores; for example, it must show z=-1.2.

- anonymous

mine did

- anonymous

http://www2.parkland.edu/businesstraining/documents/zscoretable.pdf

- mathmale

Melissa, I'm not sure what to tell you at this point. I've used my calculator and have come u p with the two areas 0.8849 and 0.1151, whose difference is 0.7698.

- anonymous

there is the link to my table

- mathmale

thank you so much for sharing that. Problem solved!!! Look up z=-1.2, and then look on that line in the column marked 0.000.

- mathmale

Your previous result came from the wrong column, the one marked 0.09.

- anonymous

0.1151?

- anonymous

oh I see

- anonymous

So I need to look for 0.00?

- mathmale

yes! So, now your results are exactly the same as the ones I've gotten from my calculator.
the area under the normal curve between z=-1.2 and z=1.2 is 0.7698.
Multiply that by the number (290) in the coin sample. What do you get?
Don't round off yet.

- anonymous

my new answer with the right numbers is 0.8849 - 0.1151 = 0.7698

- mathmale

Same here, exactly the same. multiply that by 290.

- anonymous

223.242

- mathmale

should that be rounded up or down? why?

- anonymous

I have no idea!

- mathmale

Hint: 223.4999 would be rounded down, but 223.50001 would be rounded up. If you have 223.24, would you round up or down?

- anonymous

down

- mathmale

Thanks for sticking with me thru this long procedure. Round 223.24 down to 223 (because .24 is less than 0.50). What does y our answer, 223, signify?

- anonymous

number of coins?

- mathmale

number of coins that .... what? what is the significance?

- anonymous

this is so confusing sometimes

- anonymous

that may be rejected

- mathmale

actually, 223 is the number of acceptable coins; to find the number of coins that must be rejected, subtract 223 from 290 (the total number). Result?

- anonymous

do I take that number and subtract it from the total number of coins?

- anonymous

YAY!!

- anonymous

I got 67

- mathmale

yes. 67 coins would be rejected; 223 would be accepted. congrats!
We have not discussed every detail involved in this problem, but I think you've gotten a good first exposure to the tasks at hand.

- mathmale

Have to move on. Thanks for your perseverance. Would be happy to work with you again in the future. Bye!

- anonymous

thank you!!

- mathmale

You're welcome!

- anonymous

I got it wrong?

- anonymous

it said the correct answer was 69

- mathmale

We are so close that we can assume our approaches have been correct. Different results, in a problem such as this one, are most likely due to round-off error.

- mathmale

I don't think you did anything wrong.

- mathmale

Personally I think you should move on to answering other questions, since your result was so close.

- anonymous

It wants to know if 290 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.677 and 5.857

- mathmale

Melissa: Wait.
I multiplied 290 by 0.7698 and got 223.242.
Subtracting this from 290, I got 66.758. Round that off, please.l

- mathmale

We have already answered the question you've re-typed: that probability is the area under the nomral curve between z=-1.2 and z=1.2 and is 0.7698, which rounds up to 0.77. that's a probability.

- anonymous

I got the same thing

- mathmale

Good. Then that's our answer. The prob. that the coin weights will be between z=-1.2 and z=1.2 is 0.77.

- anonymous

it said that it was 0.9998

- anonymous

I am missing something.

- mathmale

that response makes no sense to me at all. What was the question? copy and paste it here.

- anonymous

if 290 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.677 and 5.857

- mathmale

Now I see. Your 290 is a SAMPLE, not a population, and so the standard deviation is not the same as it would be for the population. Does any of this sound familiar?

- anonymous

yes. I am becoming familiar with sample vs population.

- mathmale

The sample standard deviation is \[ssd=\frac{ \mu }{ \sqrt{n} }\]

- mathmale

does that look familiar?

- anonymous

OMG!

- anonymous

NO lol

- anonymous

looks like Japanese to me!

- mathmale

;)
You already have mu, the population mean, and you know the sample size is 290.
find the ssd.

- mathmale

So, you're not Japanese? ;)

- anonymous

american girl here

- anonymous

cant read japanese or statistics lol

- anonymous

how do I have the population mean?

- anonymous

This stuff makes me feel so stupid!

- mathmale

I used to hate stats, but once I learned it in some depth, grew to like the subject.

- mathmale

Look at the original problem statement. It gives y ou the population mean and population std. dev.

- mathmale

We go thru the same thing again: calculate z scores and then calculate the area between 2 z scores.

- mathmale

the only difference is that the std. dev. we use is \[\frac{ \mu }{ \sqrt{n} }\]

- mathmale

Find the new z score if the population mean is 5.767 and the std. dev. is the sample std. dev, discussed immediately above.
You'll get 2 areas, one of which is the area to the left of your larger z score, and the other is the area to the left of your smaller z score. Subtract. The result is the probability that you were looking for.

- mathmale

I've been on OpenStudy for hours already and would like to get off now. However, you can continue to type messages about this problem to me here; either someone else or I will pick it up later on.

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