Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.32 pounds.
a) Explain why a skewed model makes sense here.
b) Explain why you cannot use a Normal model to deter-mine the probability that a largemouth bass randomly selected (“caught”) from the lake weighs over 3 pounds.
c) Each contestant catches 5 fish each day. Can you deter-mine the probability that someone’s catch averages over 3 pounds? Explain.
d) The 12 contestants competing each caught the limit of 5 fish. What’s the standard deviation of the mean weight of the 60 fish caught?
e) Would you be surprised if the mean weight of the 60 fish caught in the competition was more than 4.5 pounds? Use the 68–95–99.7 Rule.