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: -0.6
B: 48.6
C: 26
D: 2.2
E: 22.6

Answer 1

To find the percent of expenses that would fall between $184.00 and $200.00, you need to calculate the z-scores for both values and then use the standard normal distribution table. The percent is approximately 71.18%.

Step-by-step explanation:

To find the percent of expenses that would fall between $184.00 and $200.00, we need to calculate the z-scores for both values and then use the standard normal distribution table.

Step 1: Calculate the z-score for $184.00 using the formula: z = (x - μ) / σ where x is the value, μ is the mean, and σ is the standard deviation. In this case, x = $184.00, μ = $206.00, and σ = $10.00. Plugging in the values, we get: z = (184.00 - 206.00) / 10.00 = -2.20

Step 2: Calculate the z-score for $200.00 using the same formula. Plugging in the values, we get: z = (200.00 - 206.00) / 10.00 = -0.60

Step 3: Use the standard normal distribution table to find the area under the curve between -2.20 and -0.60. The area represents the percent of expenses that would fall between $184.00 and $200.00. The closest value in the table is 0.7257. Subtracting the area corresponding to -2.20 (0.0139) from the area corresponding to -0.60 (0.7257), we get: 0.7257 - 0.0139 = 0.7118

Step 4: Convert the decimal to a percentage by multiplying by 100. Therefore, the percent of expenses that would fall between $184.00 and $200.00 is approximately 71.18%.