Weighing cereal. Chocolate-coated Sugar Fun Blast cereal is filled into boxes by weight, with the weight approximately Normally distributed with an average of 16 ounces and a standard deviation of 0.2 ounces.
a. What is the probability that the box you buy (chosen at random) will weigh less than 15.5 ounces?
b. What is the probability that the box you buy will weigh between 16 and 16.25 ounces?
c. What is the probability that the box you buy will weigh more than 17 ounces?
d. What is the upper cut-off for the 90th percentile (bottom 90%) of weights?
e. What is the range for the middle 60% of weights?
f. What is the range for the upper 2.5%?