The mean daily rainfall between January 1 2007 through Janua

The mean daily rainfall between January 1, 2007, through January 1, 2009, at Pismo Beach, California, was 0.02 inches with a standard deviation of 0.11 inches. Based on this information, do you think it is reasonable to believe that daily rainfall at Pismo Beach follows a normal distribution? Explain. (Hint: Think about the possible values for daily rainfall.)

Solution

No. Any kind of distirbution of rainfall will have its own mean and standard deviation, so we cannot assume here that it already follows a normal distribution.

Furthermore, here, the mean is 0.02 in, and the standard deviation is 0.11 inches. The standard deviation is much larger than the mean!

The minimum value of rainfall is of course 0 in, so there is so little space to the left of the mean, while there are so many values to the right of the mean. Thus, from these alone, we can say that it does not follow a normal distribution.