Studies indicate that drinking water supplied by some old lead-lined city piping systems may contain harmful levels of lead. Based on data presented b

The mean lead content reading in drinking water supplied by the old piping systems in the city involving lead-lined pipes is, $\mu =0.033mg/L$ and the standard deviation is $\sigma =0.10mg/L$.
In case the reading is zero, it would mean that the particular specimen of drinking water does not have any trace of lead in it. However, a negative reading is meaningless and impossible.
According to the empirical rule, if a random variable follows normal distribution, then about 68% of the observations must lie within the interval $(\mu +-\sigma )$, about 95% of the observations must lie within the interval $(\mu \pm 2\sigma )$, and approximately all the observations must lie within the interval $(\mu \pm 3\sigma )$.
The interval $(\mu \pm \sigma )$ is calculated below:
$(\mu \pm \sigma )=(0.033—0.10,0.033+0.10)=(-0.067,0.133)$.
Note that, the interval $(\mu \pm \sigma )$ for this data set contains negative values, which is not possible according to the given scenario. Evidently, the wider intervals $(\mu \pm 2\sigma )and(\mu \pm 3\sigma )$ will also contain negative values.
This suggests that the empirical rule does not hold for the given data set.
Hence, the readings on lead content do not have a normal distribution.