Question

The amount of water dispensed by a water dispenser is normally distributed, with a mean of 12.10 ounces and a standard deviation of 0.25 ounces. In which range will the amount of water dispensed be found 99.7% of the time?

Answer 1

11.60-12.60

Explanation:

Answer 2

11.35 ounce and 12.85 ounce

Explanation:

According to the Empirial rule of the distribution under the normal curve falls within 3 standard deviations of the mean.

That is:

`\mu \pm3 \sigma`

From the given information, the mean is

`\mu = 12.10`

and the standard deviation is

`\sigma = 0.25`

We substitute the given parameters to obtain;

`12.10 \pm3(0.25)`

`12.10 \pm0.75`

This means the lower limit is

`12.10 -0 .75 = 11.35`

and the upper limit is

`12.10 + 0.75 = 12.85`

Therefore 99.7% of the amount of water dispensed is between 11.35 ounce and 12.85 ounce