The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. (a) What consumption level represents the 6th percentile? (b) What consumption level represents the 22nd percentile?(c) What consumption level represents the third quartile? mu equals 2268 kWhμ=2268 kWh sigma equals 592.2 kWhσ=592.2 kWh. A normal curve labeled u = 2268 k W h and sigma = 592.2 k W h is over a horizontal x-axis labeled Kilowatt-hours from 268 to 4268 in increments of 1000 and is centered on 2268. (a) The consumption level that represents the 6th percentile is how many kilowatt-hours? (Round to the nearest integer as needed.) (b) The consumption level that represents the 22 percentile is how many kilowatt-hours? (Round to the nearest integer as needed.) Third quartile is how many kilowatt-hours? (Round to the nearest integer as needed.)

The consumption level that represents the 6th percentile is 1347kWh. The consumption level that represents the 22nd percentile is 1811kWh. The consumption level that represents the 75th percentile is 2667kWh.

We are given a normal distribution with mean `mu=2268"kWh"` and standard deviation `sigma=592.2`. We are asked to find the consumption rate in kWh that represents the 6th percentile, the 22nd percentile, and the third quartile (which is the 75th percentile).

Since the distribution is normal, we can convert a value for the consumption to a standard normal z-score using `z=(x-mu)/sigma` . Here, we do not know x, the amount of consumption, but we can find z. Using a little algebra, we can rewrite this equation as `x=z sigma + mu` .

To find z, we consult a standard normal chart (or use technology).

(a) For the 6th percentile, this indicates that 6% of the population has this level of consumption or lower. We look for .0600 in a z-table. Using a calculator, I got `z~~-1.555` (the table will give 2 decimal places typically).

So x=(-1.555)(592.2)+2268, which is approximately 1347kWh. (This means that 6% of the population consumes a little more than one and a half standard deviations less kWh than the mean.)

(b) Similarly, for the 22nd percentile, we get `z~~-0.772`, so
`x=-0.772(592.2)+2268 ~~1811` kWh.

(c) The third quadrant is the 75th percentile (we expect z>0). From a table (or a calculator, in this case), `z~~0.674` and `x=.674(592.2)+2268~~2667`.