1. The weight of a product is normally distributed with a standard deviation of 1 ounce. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 10 ounces?
2. 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 4.46, with a standard deviation of 1.8 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 being more than 5.0.