A local fisherman is recording the time taken for him to catch a fish. From the previous data, it is known that the aver

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A local fisherman is recording the
time taken for him to catch a fish. From the previous data, it is
known that the average
time to catch a fish was 30 minutes. The fisherman assumes a
normally distributed
population with a standard
deviation of 5 minutes.
a) What is the probability that the
fisherman will catch a fish in more than 35 minutes?
b) What is the probability that the
time in which the fisherman will catch a fish is between 22 and 35 minutes?
c) From a sample of 32 fish caught, what is the
probability that the sample mean
will be less than 30.5 minutes?
d) Is the sample taken in c) assumed
to be normally distributed, why? What theorem is used to support
this assumption?