A Calgary observatory records daily the mean counting rates for cosmic rays for that day. If a daily mean rate below 3200 is considered low, then "low" values occur about 3.6% of the time (in no particular sequence). Suppose a sample of 90 mean daily counting rates is randomly selected. Consider as unusual any result that differs from the mean by more than two standard deviations. That is, unusual values are either less than σ - 2σ or greater than µ + 2σ.
a. Find the mean and standard deviation for the number of "low" daily mean rates in such groups of 90 randomly selected rates.
b. Suppose that in a 90-day period, 9 "low" values for mean daily counting rates were observed. Is this result unusual?