A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $97 and a standard deviation of $12. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $73?

a) at least 75%

b) at most 25%

c) at most 11.1%

d) at least 88.9%

Question

Mathematics

Sariah Duarte

25 April, 20:05

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $97 and a standard deviation of $12. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $73?

a) at least 75%

b) at most 25%

c) at most 11.1%

d) at least 88.9%

+1

Answers (1)

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Keyon · Answer 1

c) at most 11.1%

Step-by-step explanation:

We have the data that is 97 ± 12, with 97 being the mean and 12 the standard deviation.

Now, the percentage of people who reached them for less than 73 dollars, if it were a normal distribution:

z = (73 - 97) / 12 = - 2

so it would be, a probability of 0.0228 or 0.228%.

But we don't know what distribution it has, but we can get an idea.

A and D discarded, as they are very high values, and 73 is well below the average.

B) is still a very high value.

Therefore the answer is C, at most 11.1%