I understand that the mean $\mu \pm \sigma$ gives a better approximation of the measurements. But how is it related to the normal distribution? Is it because since $\sigma > \mu$ so the normal curve won't have a maximum at the middle anymore?
Anyway, the question is as follows, if it helps in any way:
According to the Environmental Protection Agency, chlorofoam, which in its gaseous form is suspected to be a cancer-causing agent, is present in small quantities in all the country's 240,000 public water sources. If the mean and standard deviation of the amounts of chlorofoam present in water sources are 34 and 53 micrograms per liter ($\mu g / L$) respectively, explain why chlorofoam amounts do not have a normal distribution.
Thanks in advance!