Find the probability that the yearly energy consumption of a randomly selected house is more than 1100 kWh.

Question

yearly energy consumption levels for houses are normally distributed with a mean of 1200 kWh and a standard deviation of 200 kWh. Find the probability that the yearly energy consumption of a randomly selected house is more than 1100 kWh.

Answer 1

Let x = yearly energy consumption of randomly selected hourse

what to find P(x > 1100) when mean = 1200 and SD = 200

convert x to standard normal variable z where z = (x - mean)/SD

for x = 1100, mean = 1200 and SD = 200

z = (1100 - 1200)/200 = -0.5

P(x > 1100) = P(z > -0.5) = 1 - P(z < -0.5) = 1 - 0.3085 = 0.6915