Question

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

Answer 1

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?

Answer 2

I was trying to find the z score

Answer 3

I am slow :(

Answer 4

I found the

Answer 5

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

Answer 6

yes

Answer 7

5.857 - 5.767/0.076 = 0.09/0.076= 1.2

Answer 8

right?

Answer 9

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

Answer 10

so my z scores would be 1.2 and -1.2

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

having a hard time :(

Answer 15

Which column of numbers do I look at?

Answer 16

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

Answer 17

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?

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

I found 1.2

Answer 23

now what do I look for?

Answer 24

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.

Answer 25

0.8849

Answer 26

beautiful.

Answer 27

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

Answer 28

0.0985

Answer 29

that was for -1.2

Answer 30

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

Answer 31

0.7864?

Answer 32

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 .

Answer 33

So is that my answer?

Answer 34

78 coins?

Answer 35

or would it be 79 coins?

Answer 36

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?

Answer 37

how did you get 0.7699?

Answer 38

I got 0.7864

Answer 39

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.

Answer 40

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

Answer 41

0.8849

Answer 42

0.0985

Answer 43

so I would take 0.8849 - 0.0985 = 0.7864

Answer 44

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.

Answer 45

then take hmm wonder why?

Answer 46

let me look again

Answer 47

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.

Answer 48

–1.2 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151

Answer 49

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

Answer 50

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.

Answer 51

yes. Should I use a different table?

Answer 52

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?

Answer 53

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.

Answer 54

mine did

Answer 55

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

Answer 56

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.

Answer 57

there is the link to my table

Answer 58

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.

Answer 59

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

Answer 60

0.1151?

Answer 61

oh I see

Answer 62

So I need to look for 0.00?

Answer 63

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.

Answer 64

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

Answer 65

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

Answer 66

223.242

Answer 67

should that be rounded up or down? why?

Answer 68

I have no idea!

Answer 69

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?

Answer 70

down

Answer 71

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?

Answer 72

number of coins?

Answer 73

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

Answer 74

this is so confusing sometimes

Answer 75

that may be rejected

Answer 76

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?

Answer 77

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

Answer 78

YAY!!

Answer 79

I got 67

Answer 80

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.

Answer 81

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

Answer 82

thank you!!

Answer 83

You're welcome!

Answer 84

I got it wrong?

Answer 85

it said the correct answer was 69

Answer 86

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.

Answer 87

I don't think you did anything wrong.

Answer 88

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

Answer 89

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

Answer 90

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

Answer 91

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.

Answer 92

I got the same thing

Answer 93

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.

Answer 94

it said that it was 0.9998

Answer 95

I am missing something.

Answer 96

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

Answer 97

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

Answer 98

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?