Central limit therom

Question

According to records of Commonwealth Edison, monthly electric consumption for January follows a
normal distribution with a mean of 1,650 kilowatt hours, and a standard deviation of 320 kilowatt hours.

Commonwealth Edison wants to identify its heaviest users, which are those that are in the top 6% of
electric consumption. How many kilowatt hours in January would qualify for the heavy user classification?

Answer 1

"According to records ... follows a normal distribution" The fact of a normal distribution is given by hypothesis, not by the Central Limit Theorem here.

 

The Central Limit Theorem is when it isn't a given that the distribution is normal, and then it has to do with sampling.

 

Here, find the z-value corresponding to 100%-6% = 94% (that is, the z-value such that 94% of the area under the normal distribution is to the left of the point z standard deviations to the right of mean). Multiply that z value by the standard deviation of 320, then add that to 1650.

 

I get a z of about 1.555, giving 1650 + 1.555*320 = 2147.6 kwh

 

Remember: the central limit theorem has to do with sampling from a distribution, that is, taking n many samples from the population, and computing the distribution of the sample means.

 

I hope that helps.