The warehouse for a hardware store chain has just received a truckload of 5000 electric drills. Before accepting the shipment, the purchasing manager insists that a sample of the drills be randomly selected for testing. He intends to measure the maximum power consumption of each drill. He will reject the shipment if the mean consumption for the sample is greater than 300 watts as listed on the product label. Accompanying the shipment is the manufacturer's records of product tests showing the drills on the truck require an average of 295 watts with a standard deviation of 16 watts. Assume normal distribution of power consumption for population of drills.
a. Find the probability that the truckload of drills will be rejected if he samples 25 drills.
b. Find the probability that the truckload of drills will be rejected if he samples 49 drills
c. What are the impacts of larger sample size n on the mean and standard deviation among sample averages of power consumption (and) and its absolute values of z-score?