Question: During the past 10 years, Minnesota Pollution Control Agency has measured the concentration of chlorophyll-a in Lake Calhoun 64 times. The mean concentration 2' was 3.6 parts per billion (ppb). It is known that the standard deviation σ was 1.6 ppb.
Is this a firm evidence that the the mean concentration of chlorophyll-a in Lake Calhoun is greater than 3.0 ppb? Answer your question by computing Pr(X‾ > 3.6 | μ= 3.0). Assume that the distribution of chlorophyll-a concentration is normal.