91影视

There is a study of a major metropolitan hospital. The study revealed that in every 100 medications prescribed or dispensed, 1 is an error. But there is 1 error from a significant problem in every 500 medications. The hospital prescribed or dispensed 60000 medications per year.

Consider the probability of having an error $p=\frac{1}{100}=0.01$.

And the probability of having a significant error $p_s=\frac{1}{500}=0.002$.

a.

The expected proportion of error per year of the hospital is,

$\begin{array}{c}渭=np\\ =60000脳0.01\\ =600\end{array}$

The expected proportion of significant error per year of the hospital is,

$\begin{array}{c}{渭}_s=n{p}_s\\ =60000脳0.002\\ =120\end{array}$

The limit of the expected proportion significant error per year fall is, $\left(p_s卤2\sqrt{\frac{p_s\left(1鈭�p_s\right)}{n}}\right)$.

So,

$\begin{array}{c}\left(p_s卤2\sqrt{\frac{p_s\left(1鈭�p_s\right)}{n}}\right)=\left(0.002卤2脳\sqrt{\frac{0.002脳\left(1鈭�0.002\right)}{60000}}\right)\\ =\left[\left(0.002鈭�2脳\sqrt{\frac{0.002脳\left(1鈭�0.002\right)}{60000}}\right),\left(0.002+2脳\sqrt{\frac{0.002脳\left(1鈭�0.002\right)}{60000}}\right)\right]\\ =\left[\left(0.002鈭�0.000364\right),\left(0.002+0.000364\right)\right]\\ =\left[0.00164,0.00236\right]\end{array}$

Thus, the required limit is $\left[0.00164,0.00236\right]$$\left[0.00164,0.00236\right]$.