A public utility company monitors the daily electricity consumption of a city. The consumption follows a normal distribution with a mean of 500 MW and a standard deviation of 20 MW.

Approximately what percentage of days will have a consumption between 460 MW and 540 MW?

Answer options:

68%

95%

99.7%

50%

How to approach this question

Determine how many standard deviations away from the mean the values 460 and 540 are. Apply the empirical rule (68-95-99.7).

Full Answer

B.95%✓ Correct

The range 460 MW to 540 MW represents the mean +/- 40 MW. Since the standard deviation is 20 MW, this is exactly +/- 2 standard deviations. According to the empirical rule of normal distribution, approximately 95% of data falls within 2 standard deviations of the mean.

Common mistakes

Confusing the empirical rule percentages (e.g., selecting 68% which is 1 SD).

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