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

Question

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

anonymous · Answer

@sweetburger

anonymous · Answer

@UsukiDoll

usukidoll · Answer

I haven't studied statistics. Sorry :/

anonymous · Answer

is okay

phi · Answer

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 · Answer

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 · Answer

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

phi · Answer

people use a z table.

anonymous · Answer

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

anonymous · Answer

so i got C but i dont think that is correct

phi · Answer

you are looking for the area 
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