A recent survey was conducted 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 $143 and a standard deviation of
$8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes
Will have a monthly utility bill of more than $135?
A)approximately 34%
B)approximately 84%
C)approximately 16%
D)approximately 95%

Question

Quizplus · Accepted Answer

Given the distribution is mound-shaped and symmetric (which suggests a normal distribution), we can use the empirical rule or z-scores to find the percentage. A bill of $135 is 1 standard deviation below the mean ($143 - $135 = $8, and the standard deviation is $8). According to the empirical rule, 68% of the data falls within 1 standard deviation of the mean, so 34% is on each side. Since we're looking for more than $135, we take the upper 50% + 34% = 84%.

A Recent Survey Was Conducted to Compare the Cost of Solar