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 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 $94 and a standard deviation of $12. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of more than $82?
A) approximately 16%
B) approximately 95%
C) approximately 32%
D) approximately 84%

Question

Quizplus · Accepted Answer

Using the empirical rule for a bell-shaped distribution, a monthly utility bill of more than $82 is within one standard deviation below the mean ($94 - $12 = $82). According to the empirical rule, 68% of the data falls within one standard deviation of the mean, so 100% - 68% = 32% is outside one standard deviation. Since the distribution is symmetrical, half of this 32% (16%) would be below $82, leaving approximately 84% above $82.

Solar Energy Is Considered by Many to Be the Energy