Charanka Solar Park in India reports that it produces an average of 16,400 kilowatt hours (kwh) of electricity per day, with a standard deviation of 2200 kwh.If this electrical output has a normal distribution, for what proportion of days would we expect the day's output to be between 15000 and 18000 kwh?
A).4520
B).6535
C).4421
D).5062
E).3879

Question

Quizplus · Accepted Answer

To find the proportion of days with output between 15,000 and 18,000 kwh, we calculate the z-scores for these values and then find the corresponding proportions in the standard normal distribution. For 15,000 kwh: $Z = \frac{15000 - 16400}{2200} = -0.636$For 18,000 kwh: $Z = \frac{18000 - 16400}{2200} = 0.727$Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the proportions of 0.2623 and 0.7655, respectively. The difference between these values gives the proportion of days with output between 15,000 and 18,000 kwh, which is $0.7655 - 0.2623 = 0.5032$ or 50.32%. This corresponds to choice D.

Charanka Solar Park in India Reports That It Produces an Average