Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare thecost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution ofthe amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $120and a standard deviation of $11. If the distribution can be considered bell shaped, what percentage of homeswill have a monthly utility bill of more than $109?
A) approximately 84%
B) approximately 95%
C) approximately 16%
D) approximately 32%

Question

Quizplus · Accepted Answer

Using the empirical rule for a bell-shaped distribution, a score of $109 is one standard deviation below the mean ($120 - $11 = $109). According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, leaving 32% outside. Since the question asks for the percentage of homes with bills more than $109, we consider the upper half of the remaining percentage, which is half of 32%, or 16%, added to the 68% within one standard deviation. This gives us 84%.

Solar Energy Is Considered by Many to Be the Energy