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. Inwhich range will the amount of water dispensed be found 95% of the time?A. 11.45 ounces to 11.75 ouncesB. 11.30 ounces to 11.90 ouncesC. 11.15 ounces to 12.05 ouncesD. 11.00 ounces to 12.20 ounces

Answer 1

We know by the empirical rule of the distribution under the normal curve falls within 3 standar deviations of the mean. This is:

$\mu\pm3\sigma$

In this case, we have the following:

$\begin{gathered} \mu=11.60 \\ \sigma=0.15 \end{gathered}$

Doing the substitution we have:

$\begin{gathered} \mu\pm3\sigma \\ \Rightarrow11.60\pm3(0.15) \\ \Rightarrow11.60\pm0.45 \\ \Rightarrow(11.60-0.45,11.60+0.45) \\ \Rightarrow(11.15,12.05) \end{gathered}$

therefore 95% of the amount of water dispensed is between 11.15 ounces and 12.05 ounces