Tim Worker is doing his budget. He discovers that the average electric bill for the year was $206.00 with a standard deviation o
f $10.00. What percent of his expenses in this category would he expect to fall between $184.00 and $200.00?
The z for $184.00 = -
The percent of area associated with $184.00 = %
The z for $200.00 = -
The percent of area associated with $200.00 = %
Subtracting the two percentages, the percent of expenses between $184.00 and $200.00 is %
The z for $184.00 = -
The percent of area associated with $184.00 = %
The z for $200.00 = -
The percent of area associated with $200.00 = %
Subtracting the two percentages, the percent of expenses between $184.00 and $200.00 is %
1 answer:
Answer:
- -2.2
- 1.4%
- -0.6
- 27.4%
- 26%
The z-value is computed from ...
... z = (x -µ)/σ
... z = (184 -206)/10 = -2.2 . . . . for $184
... z = (200 -206)/10 = -0.6 . . . . for $200
You can look up these values in a normal distribution table, or you can use an appropriate calculator to find the corresponding percentiles.
... -2.2 corresponds to the 1.390 percentile. (That amount of area is below -2.2 standard deviations from the mean.)
... -0.6 corresponds to the 27.425 percentile.
Subtracting the two percentages gives the percentage of expenses between $184 and $200. That number is 26.035% ≈ 26%.
_____
<em>Comment on the calculator display</em>
The difference that got cut off from the display in the attachment is ...
... 0.2603496703
The <em>normalcdf( )</em> function requires a lower limit. Using -8 standard deviations is effectively equivalent to -∞ for this purpose, as any lower number has no effect on the least-significant digits of the result.
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