10. Use the mean and standard deviation to sketch a normal distribution and use the Empirical Rule to label the areas.

NORMAL DISTRIBUTION

For the 156 BGE bills collected, the average of the average monthly temperatures is 57.2° and the standard deviation is 15.9°.

  1. Use the mean and standard deviation to sketch a normal distribution and use the Empirical Rule to label the areas.

 

  1. Using the distribution just sketched, identify the two average monthly temperatures that would separate usual from unusual

 

  1. What would be the Z-score for a temperature of 75°? What percent of the bills had average monthly temperatures higher than this value?

 

  1. What temperature would have a Z-score of -1.25? What percent of the bills had average monthly temperatures below this value?

 

  1. What average monthly temperature values would identify the middle 80% of the bills?

 

  1. 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.

 

  1. 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.

 

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