Question

Tim Worker is doing his budget. He discovers that the average electric bill for the year was $206.00 with a standard deviation of $10.00. What percent of his expenses in this category would he expect to fall between $184.00 and $200.00?

a) -.6
b) 48.6
c) 26
d) 2.2
The z for $184.00 =
a) 2.2
b) .6
c) 26
d) 22.6
The percent of the area associated with $184.00 =
a) 2.2
b) .6
c) 26
d) 22.6
The z for $200.00 =
a) .6
b) 48.6
c) 22.6
d) 26
The percent of the area associated with $200.00 =
a) 48.6
b) 2.2
c) 22.6
d) .6
Subtracting the two percentages, the percent of expenses between $184.00 and $200.00 is
a) 22.6
b) 48.6
c) .6
d) 2.2
e) 26

Answer 1

The percentage of Tim Worker's electric bills that fall between $184.00 and $200.00 is approximately 25.6%. The closest provided answer to the calculated percentage is 26%.

Step-by-step explanation:

Tim Worker is looking to understand what percent of his electric bills would fall between $184.00 and $200.00 given an average bill of $206.00 with a standard deviation of $10.00. To determine this, we calculate the z-scores for both $184.00 and $200.00 and then find the percent of the area under the normal curve that corresponds to these z-scores.

The z-score for $184.00 is found by taking (amount - average) / standard deviation, which is (184 - 206) / 10, giving us a z-score of -2.2. The z-score for $200.00 is calculated as (200 - 206) / 10, resulting in a z-score of -0.6.

Using the standard normal distribution table, we find the percent of the area associated with a z-score of -2.2, which is approximately 1.4%. Similarly, the area associated with a z-score of -0.6 is roughly 27%. Therefore, subtracting the smaller area from the larger gives us the percent of expenses falling between $184.00 and $200.00, which is 27% - 1.4% = 25.6%. Since the choices do not provide this exact value, the closest choice to this calculated percentage is 26%.