The mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.5%. Assume that a sample size of 40 people was surveyed from the population an infinite number of times.

95% of the sample mean occurs between:
A. 55.89%
B. 56.07
C. 56.45
and
A. 57.55%
B. 57.93%
C. 58.11%.

Question

The mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.5%. Assume that a sample size of 40 people was surveyed from the population an infinite number of times.

95% of the sample mean occurs between:
A. 55.89%
B. 56.07
C. 56.45
 and 
A. 57.55%
B. 57.93%
C. 58.11%.

anonymous · Answer

@pooja195

anonymous · Answer

@Luigi0210

anonymous · Answer

@Mehek14

anonymous · Answer

Please help I dont know what standard deviation is either

anonymous · Answer

@steve816

anonymous · Answer

@tkhunny

aihberkhan · Answer

Okay. 

Looking at the problem we have to find the mean of the sample means, which is $57$% or $0.57$. 

Now, to find the standard deviation of the sample means you would do $(0.035/\sqrt{40})$, which equals $0.0055$
 
So, the $95$% sample means interval is 

$0.57 - 1.96(0.0055)$ for the Lower Limit

and 

$0.57 + 1.96(0.0055)$ for the Upper Limit

anonymous · Answer

@zepdrix

aihberkhan · Answer

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anonymous · Answer

Thanks for the help. To clarify, did I select the correct answers?

anonymous · Answer

@AihberKhan

aihberkhan · Answer

Can you show me all the choices for both? :)

@Spikers

anonymous · Answer

95% of the sample mean occurs between:
A. 55.89%
B. 56.07
C. 56.45
 and 
A. 57.55%
B. 57.93%
C. 58.11%.

aihberkhan · Answer

I actually think it is $.56446$ to $.57553$ I just found another site with your question, maybe it can help clarify. Check this out: http://openstudy.com/updates/524af233e4b06f86e820bae2 Also, you might want to ask someone else to double check :) I can help tag people for you :)

aihberkhan · Answer

@Conqueror 

Please double check that my answer to his questions is right :)

aihberkhan · Answer

@tkhunny 

Please double check that my answer to his questions is right :)

aihberkhan · Answer

@xapproachesinfinity 

Please double check that my answer to his questions is right :)

aihberkhan · Answer

@Mehek14 

Please double check that my answer to his questions is right :)

anonymous · Answer

Yeah I'm kinda confused as to which the correct answers are

anonymous · Answer

@pooja195

anonymous · Answer

@TheSmartOne