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

Answer:

11.35 ounce and 12.85 ounce

Step-by-step 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