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) 22.6%
b) 48.6%
c) 26%
d) 2.2%

Answer 1

To find the percentage of Tim Worker's electrical expenses between $184 and $200, we calculate the Z-scores for these values and then determine the corresponding percentiles. Subtracting these percentiles, we find that approximately 26% of his electrical expenses would be in this range.

Step-by-step explanation:

To determine what percent of Tim Worker's electrical expenses would fall between $184.00 and $200.00, we will need to use the concept of normal distribution and Z-scores.

First, we calculate the Z-scores for the values $184 and $200 using the formula:

Z = (X - μ) / σ

For $184:

Z = (184 - 206) / 10

Z = -2.2

For $200:

Z = (200 - 206) / 10

Z = -0.6

Next, we look up these Z-scores in a standard normal distribution table or use a statistical calculator to find the corresponding percentiles. The value for Z = -2.2 corresponds to approximately 1.39%, and the value for Z = -0.6 corresponds to approximately 27.43%.

To find the percentage of expenses between these two Z-scores, we subtract the lower percentile from the higher percentile:

27.43% - 1.39% = 26.04%

Therefore, Tim Worker would expect approximately 26% of his electrical expenses to fall between $184.00 and $200.00.