8.22 It is known from past samples that pH of water in Bolton Creek tends to be approximately normally distributed. The average water pH level of water in the creek is estimated regularly by taking 12 samples from different parts of the creek.

Assuming they represent random samples from the creek, find the approximate probability that the sample mean of the 12 pH measurements will be within 0.2 unit of the true average pH for the field. The most recent sample measurements were as follows:

6.63, 6.59, 6.65, 6.67, 6.54, 6.13, 6.62, 7.13, 6.68, 6.82, 7.62, 6.56