# 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?

Mar 28, 2018

p ~~ .1913 ~~ 19%

#### Explanation:

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

Find probability $p$ that energy is between $1100 k W , 1221 k W$

Find the z-scores of each energy level: $z = \frac{x - \mu}{\sigma}$

${z}_{1} = \frac{1100 - 1050}{218} \approx 0.2294$

${z}_{2} = \frac{1221 - 1050}{218} \approx 0.7844$

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

${z}_{1} \approx 0.2294 \approx 0.23 \implies {p}_{1} = .5910$

${z}_{2} \approx 0.7844 \approx 0.78 \implies {p}_{2} = .7823$

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

p_2 - p_1 = .1913 ~~ 19%