Question

the city electric company reported that the average amount of energy used per household each month in the last year was 7.5 btus. employees from the department randomly sampled 100 homes in the community and reviewed the electric bills for the recent month. which of the following would most likely be true of the electric consumption of the 100 households?
a fifty of the households will have used more than 7.5 btus, and 50 of the households will have used less than 7.5 btus.
b each household will have used at most 7.5 btus.
c fifty of the households will have used exactly 7.5 btus, and 50 of the households will have used more or less than 7.5 btus.
d each household will have used at least 7.5 btus.
e each household will have used exactly 7.5 btus.

Explanation:

The average (mean) energy use is 7.5 BTUs for 100 households. The mean is a measure of central tendency, and in a sample, values are distributed around the mean. Option A is incorrect because the mean doesn't imply an exact 50 - 50 split of values above and below (e.g., in skewed distributions, this isn't true). Options B, D, and E are wrong because the mean doesn't mean each household uses at most, at least, or exactly the mean (individual values can vary above or below the mean). Option C is also incorrect as the mean doesn't imply 50 households use the exact mean. Wait, no—wait, actually, re - evaluating: The original question's options might have a typo, but among the given options, none are completely correct, but if we assume a symmetric distribution (like normal) as a rough approximation, the closest idea is that around half are above and half below the mean. Option A is the only one that captures the idea of a split around the mean (even though in reality it's not always exactly 50 - 50, but among the options, it's the most reasonable). Wait, no—actually, the mean is the average, so some households use more, some less, and the average is 7.5. So the idea that about half are above and half below (even if not exactly 50) is what option A is trying to say. The other options (B: all ≤7.5, D: all ≥7.5, E: all =7.5, C: 50 exactly 7.5) are all incorrect because individual values can deviate from the mean. So option A is the best among the given choices as it reflects the concept that the mean is a central value with values distributed around it (some above, some below).

Answer:

A. Fifty of the households will have used more than 7.5 BTUs, and 50 of the households will have used less than 7.5 BTUs.