1. Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the sample survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $117 and a standard deviation of $13.

a. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of less than $104?

b. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of less than $156?

c. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of above $130?

d. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill between $104 and 130?

e. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill between 78 and 91?

f. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill between $78 and $156?

g. What would be the z-score for a monthly utility bill of $118 (round to two decimal places). Do you think this household should switch to solar? Briefly explain.

2.After the LA marathon two runners where comparing their z-score. Runner one had a z-score of -1.34 and runner two had a z-score of -1.24. Which runner had a better time?