# Central limit theorem question?

According the International Atomic Energy Agency, electricity per-capita consumption in Canada is 16,939 kwh in 2002. A random sample of 53 households is monitored for one year to determine electricity usage. If the population standard deviation of annual usage is 3,500 kwh, what is the probability that the sample mean will be each of the following?

Less than 16,000 kwh

Less than 15,000 kwh

As population mean = 16939 n=53 SD=3500 sample SD=480.76197

I got p(z<16000)=-1.95 0.4744 0.5-04744=0.02560

but it is not correct

and if the sample mean is less than 15000, z score= -4.03318 the number is not on the data.

How can I solve this question? help me please

### 2 Answers

- 6 years agoFavorite Answer
Xbar < 16000;

so Z score = [16000 - 16939] / 480.762 = - 1.95

P(Z<= -1.95) = 0.02559

Your answers are correct.

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- cidyahLv 76 years ago
First is correct.

Second is correct.

P( z < -4.03318) = 0.0000 (almost 0)

If you want an exact answer:

P( z < -4.03318) = 2.75135 x 10^(-5) ( Excel)

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