For the 156 BGE bills collected, the average of the average monthly temperatures is 57.2° and the standard deviation is 15.9°.
- Use the mean and standard deviation to sketch a normal distribution and use the Empirical Rule to label the areas.
- Using the distribution just sketched, identify the two average monthly temperatures that would separate usual from unusual
- What would be the Z-score for a temperature of 75°? What percent of the bills had average monthly temperatures higher than this value?
- What temperature would have a Z-score of -1.25? What percent of the bills had average monthly temperatures below this value?
- What average monthly temperature values would identify the middle 80% of the bills?
- Given that the percentage of bills having a high average monthly temperature is 21%, and that the process of selecting bills is considered binomial, if the random variable X represents the number of bills with high average monthly temperatures, show why this distribution can be approximated with the normal distribution.
- Extra Credit: Knowing that the binomial distribution in #15 can be approximated with the normal distribution, find P(30 < x < 40), the probability of randomly selecting between 30 and 40 bills that have high average monthly temperatures.