G 293 households were surveyed as part of a study on gas consumption. Water usage per day per household follows a normal distribution. The mean water usage per day per household in this survey was 40 gallons, and a 95.44% of the data falls within the interval (32.5, 47.5). What is the variance?

The variance is 14.0625 square gallons.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 40 gallons

We are given that the distribution of gas consumption is a bell shaped distribution that is a normal distribution.

About 95.44% of the data falls within the interval (32.5, 47.5).

Empirical Rule:

Thus, we can write,

Putting the values, we get,

Solving, we get

Thus, the standard deviation of water usage per day per household is 7.5

The variance can be calculated as:

The variance is 14.0625 square gallons.

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