2) The volume of water in swimming pools in a local neighborhood are normally distributed. What is the percentage of volumes that are within 3 standard deviation of the mean?

The percentage of  volumes that are within 3 standard deviation of the mean is 99.73%.

Step-by-step explanation:

We want to calculate the area under the curve within 3 standard deviations from the mean.

If we use the standard normal distribution, this probability can be calculated as the diference between P(z<3) and P(z<-3).

The area under the curve for the standard distribution and for any normal distribution within 3 standard deviation from the mean is 0.9973.

The percentage of  volumes that are within 3 standard deviation of the mean is 99.73%.

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