Question

The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilowatt-hours. Random samples of size 35 are drawn from this population. Find (a) the mean and (b) the standard deviation of the sampling distribution of sample means. Round the answer from part (b) to the third decimal place.

Answer 1

a) 471.5 kilo-watt hours.

b) 31.76 kilo-watt hours

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the population:

Mean 471.5 kilo-watt hours.

Standard deviation of 187.9 kilowatt-hours.

For the sample:

Sample size of 35, by the Central Limit Theorem:

a) Mean

471.5 kilo-watt hours.

b) Standard deviation

`s = (187.9)/(√(35)) = 31.76`

31.76 kilo-watt hours