Question

He per capta energy consumption level (in kilowat-hours) in a certain country for a recent year can be approwimated by a normal distribution, as shown in ne figure.

(a) What consumplion level represonts the 7th percentie?
(b) What consumption level reprosents the 16th percentle?
(c) What consumption level repretents the third quarble?

(a) The cortunction level that represents the 7 percensie is kiowath-hours.
(Pound to the nearect intoget as ceeded)

Answer 1

To find the consumption level at different percentiles, use the z-score formula and standard normal distribution table.

Step-by-step explanation:

(a) What consumption level represents the 7th percentile?

To determine the consumption level that represents the 7th percentile, first find the corresponding z-score using the standard normal distribution table. The z-score for the 7th percentile is -1.405. Next, use the z-score formula to find the consumption level. Assuming a mean energy consumption level of μ and a standard deviation of σ, the formula is: x = μ + z * σ. Plug in the values and calculate the consumption level.

(b) What consumption level represents the 16th percentile?

Follow the same steps as in part (a) to find the z-score for the 16th percentile. The z-score is -0.994. Use the z-score formula to find the consumption level.

(c) What consumption level represents the third quartile?

The third quartile corresponds to the 75th percentile. The z-score for the 75th percentile is 0.674. Use the z-score formula to find the consumption level.