Question

Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Using only the values of these two parameters and your knowledge of the properties of the Normal distribution, give an argument why it is unreasonable to assume that the time between arrivals of buses is normally distributed (or even approximately so). (Hint: Consider the range of data of a Normal distribution.)

Answer 1

Solution:

Given a distribution with

mean = 8.7

Standard deviation = 8.7

Let us assume that the distribution is normal

For the normal distribution, about 99.7% i.e. almost all the observations fall within 3 standard deviations of the mean.

i.e. within   - 3 and + 3

i.e. within 8.7 - 3 * 8.7 and 8.7 + 3 * 8.7

i.e. within -17.4 and 34.8

Since the normal is the symmetric distribution and range of data is  within -17.4 and 34.8 then there must be several negative values in the data.

But the data represents the times between arriving patients which can not be negative values.

So , our assumption is incorrect . So,  it is unreasonable to assume that the time between arrivals of buses is normally distributed (or even approximately so).