Question 1: A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.5 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 36 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes is greater than 4.35.
Question 2: Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.25 ounces. The weights of the sugar bags are normally distributed. What is the probability that 25 randomly selected packages will have an average weight in excess of 16.06 ounces?