A clinic has an average of 120 visiting patients per day nor

A clinic has an average of 120 visiting patients per day (normally distributed) with variance of 64 patients. A manager of the clinic desires to be able to serve at least 95% of all patients who visit the clinic. What number of patients must the clinic be able to serve in order to meet 95% of daily patient demand?

Solution

for this we plot a normal distribution curve-

For the present example, the sampling distribution of the mean has a mean of 120 and a standard deviation of = 8. Note that the standard deviation of a sampling distribution is its standard error. Figure 1 shows this distribution. The shaded area represents the middle 95% of the distribution and stretches from 104.32 to 135.68. These limits were computed by adding and subtracting 1.96 standard deviations to/from the mean of 120 as follows:

120 - (1.96)(8) = 104.32
120 + (1.96)(8) = 135.68

The value of 1.96 is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean

Hence,it must serve 105 to 135 patients to meet 95% daily patient demand