6. 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 u = 10.2 inches and standard deviation o = 1.4 inches. a) What is the probability that a single trout taken at random from the pond is between 8 and 12 inches long? That's find P(8 < x < 12) b) What is the probability that the mean length x of five trout taken at random is between 8 and 12 inches long? That's find P(8

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6. 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 u = 10.2 inches and standard deviation o = 1.4 inches.
a) What is the probability that a single trout taken at random from the pond is between 8 and 12 inches long?
That's find P(8 < x < 12)
b) What is the probability that the mean length x of five trout taken at random is between 8 and 12 inches long?
That's find P(8<I<12) (Hint: Your standard deviation here should be )
c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would
this?
you expect
Transcribed Image Text:6. 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 u = 10.2 inches and standard deviation o = 1.4 inches. a) What is the probability that a single trout taken at random from the pond is between 8 and 12 inches long? That's find P(8 < x < 12) b) What is the probability that the mean length x of five trout taken at random is between 8 and 12 inches long? That's find P(8<I<12) (Hint: Your standard deviation here should be ) c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would this? you expect
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