Answer:
a. 0.1971
Step-by-step explanation:
Z score is used to measure by how many standard deviations the raw score is above or below the mean. It is given by the formula:
[tex]z=\frac{x-\mu}{\sigma}\\ \\Where\ \mu=mean, x=raw\ score, \sigma=standard\ deviation[/tex]
Given that:
μ = 1050 kWh, σ = 218 kWh
For x = 1100 kWh
[tex]z=\frac{x-\mu}{\sigma}=\frac{1100-1050}{218} =0.23[/tex]
For x = 1225 kWh
[tex]z=\frac{x-\mu}{\sigma}=\frac{1225-1050}{218} =0.80[/tex]
From the normal distribution table, P(1100 < x < 1225) = P(0.23 < z < 0.8) = P(z < 0.8) - P(z < 0.23) = 0.7881 - 0.5910 = 0.1971
