Question

The energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. How do you find the probability that the energy consumption level is between 1100 kWh and 1221 kWh?

Answer 1

`p ~~ .1913 ~~ 19%`

Explanation:

Given: normal distribution, `mu = 1050; sigma = 218`

Find probability `p` that energy is between `1100 kW, 1221 kW`

Find the z-scores of each energy level: `z = (x- mu)/(sigma)`

`z_1 = (1100 - 1050)/218 ~~ 0.2294`

`z_2 = (1221 - 1050)/218 ~~ 0.7844`

Look up the probabilities of each z-score from a z-table:

`z_1~~ 0.2294 ~~0.23 => p_1 = .5910`

`z_2 ~~0.7844 ~~0.78 => p_2 = .7823`

The probability that the energy level is between these two values is

`p_2 - p_1 = .1913 ~~ 19%`