The Southern California Earthquake data center recorded over 10,594 earthquakes of at least 1.0 on the Richter scale in Southern California over the span of one year. From a random sample of 40 of the recorded earthquakes, the mean size of an earthquake was found to be 2.57 with a standard deviation of 0.65. Estimate the average size of an earthquake in the Southern California region with 99% confidence.
confidence multiplier/critical value for 99% confidence level to 3 decimals:
We are 99% confident the average size of an earthquake recorded in the Southern California region that year is between () and () on the Richter Scale.