A city has 1,162,529 residents. A recent census showed that 307,944 of these residents regularly use the city’s

public transportation system. A survey is being conducted in which 1,084 of the city’s 1,162,529 residents will be randomly selected.

This question relates to the number (not proportion) of people in the survey that is made up of people that do use the city’s public transport.

The number of people in the survey that do use public transport approximately follows a normal distribution. Calculate the standard deviation of this distribution. Give your answer rounded to 2 decimal places.

Standard deviation =

Note: when the question was about the proportion of people the answer was:

π =k/N 

=377,788/1,179,998 = 0.32015986…

Of the people in the sample of n = 1,093 residents, the proportion that use public transport follows the sampling distribution of the proportion. This distribution is approximately the normal distribution with mean   and standard deviation √( (1 –  )/n).

Therefore the standard deviation of this distribution is √((  × (1 –  ))/n) = √((0.32015986… × (1 – 0.32015986…))/1,093) = 0.01411162… ≈ 0.0141.

The question I need help with asks for relates to the number of people, not proportion, therefore the calculation has to be different. 

Thanks!

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