Use the Empirical Rule to Describe Data That Are Bell Shaped
-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 $\$ 119$ and a standard deviation of $\$ 8$. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of more than $\$ 111$ ?
A) approximately $84 \%$
B) approximately $95 \%$
C) approximately $16 \%$
D) approximately $32 \%$

Question

Quizplus · Accepted Answer

Given a bell-shaped distribution, the Empirical Rule (68-95-99.7 rule) can be applied. A monthly utility bill of $111 is one standard deviation below the mean ($119 - $8 = $111). According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, about 34% are below $111 and 34% are between $111 and $119, leaving approximately 100% - 34% = 66% above $111. However, since we also include the middle 34%, the correct percentage is 34% + 66% = 100% - 34% = 66%. The error in the calculation needs correction: the correct interpretation is that approximately 84% (50% + 34%) of homes will have a monthly utility bill of more than $111, considering the distribution on both sides of the mean.

Use the Empirical Rule to Describe Data That Are Bell $119\$ 119$119

Use the Empirical Rule to Describe Data That Are Bell $\$ 119$