Suppose the number of students in a class for the Business Statistics program at a University has a mean of 23 with a standard deviation of 4.3. If 15 classes are selected randomly, find the probability that the mean number of students is between 20 and 30.
0.9699
0.9966
0.8412
0.6824

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- anonymous

- anonymous

- UsukiDoll

I haven't studied statistics. Sorry :/

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## More answers

- anonymous

is okay

- phi

These are the population statistics:
mean of 23 with a standard deviation of 4.3.
\[ \mu = 23 ,\ \ \sigma= 4.3\]
15 classes are selected randomly
represent a sample of size 15. The mean of this sample is also 23,
but with a standard deviation \( \sigma_{sample}= \frac{1}{\sqrt{15}} \sigma\)

- phi

the std dev of your sample means will be 4.3/sqrt(15) = 1.11
the limits 20 to 30 represent
-3/1.11 to +7/1.11 or -2.7 to +6.3 std dev
as the +6.3 above the mean is very far out in the tail, you can just find the area under the curve from -2.7 to infinity
(or 1 - area below -2.7)

- anonymous

@phi and how would you find the area under the curve ?

- phi

people use a z table.

- anonymous

so can i find it and tell you my answer to see if i get it right ?

- anonymous

so i got C but i dont think that is correct

- phi

you are looking for the area
|dw:1437654513070:dw|

- phi

can you post a copy of the table you are using ?

- anonymous

i dont have one i just looked one up in google

- anonymous

i honestly just dont get this and i already went back to the lesson like 3 times to see if i could figure it out and i cant.

- phi

what is the link to the table?

- anonymous

http://cosstatistics.pbworks.com/f/1281154582/6368.png

- anonymous

wait would it be B ?

- phi

the area you want for your problem starts at -2.7 and goes to the right
your table shows the area starting on the left and going up to some std dev.
this is opposite of your problem.
BUT, because the curve is symmetric, you can use this table.
find the value for z= 2.7

- anonymous

so where it say 2.7 i got there ?

- phi

yes

- anonymous

i got 0.9966

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