Probability regarding x and
Suppose a team of biologists has been studying the Pinedale children’s fishing pond. Let x represent the length of a single trout taken at random from the pond. This group of biologists has determined that x has a normal distribution with mean μ = 10.2inches and standard deviation σ = 1.4inches.
(a) What is the probability that a single trout taken at random from the pond is between 8 and 12 inches long?
(b) What is the probability that the mean length of five trout taken at random is between 8 and 12 inches?
(c) Looking at the results of parts (a) and (b), we see that the probabilities (0.8433 and 0.9977) are quite different. Why is this the case?
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