Question

The amount of water dispensed by a water dispenser is normally distributed,
with a mean of 11.60 ounces and a standard deviation of 0.15 ounces. In
which range will the amount of water dispensed be found 99.7% of the time?

Answer 1

Using the Empirical Rule, the amount of water dispensed will be found 99.7% of the time in the range of 11.15 ounces and 12.05 ounces.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

The mean and the standard deviation are given, respectively, by:

11.6 ounces and 0.15 ounces.

The bounds within 3 standard deviations of the mean, corresponding to 99.7% of the interval, are given as follows:

• 11.6 - 3 x 0.15 = 11.15 ounces.

• 11.6 + 3 x 0.15 = 12.05 ounces.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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