Question 384272: A team of biologist has been studying the childrens fishing pond in Fall-River. Let x represent the length of a single tilapia taken at random from the fishing pond. This group of the biologists has determined that x has a normal distution with mean u equals 10.2 inches and standard deviation o equals 1.4 inches.
i.) what is the porbability that a single tilapia selected at random from the pond is between 8 and 12 inches long?
ii.) what is the probability that the mean length x (bar) of five tilapia taken from at random from the pond is between 8 and 12 inches?
iii.) Is the result in parts a and b the same of different?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A team of biologists has been studying the childrens fishing pond in Fall-River. Let x represent the length of a single tilapia taken at random from the fishing pond. This group of the biologists has determined that x has a normal distribution with mean u equals 10.2 inches and standard deviation o equals 1.4 inches.
i.) what is the probability that a single tilapia selected at random from the pond is between 8 and 12 inches long?
Using a TI calculator I get:
Ans: Normalcdf(8,12,10.2,1.4) = 0.8427
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ii.) what is the probability that the mean length x (bar) of five tilapia taken from at random from the pond is between 8 and 12 inches?
Ans: normalcdf(8,12,10.2,1.4/sqrt(5)) = 0.9978
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iii.) Is the result in parts a and b the same or different?
Different because the standard deviation for the mean of the sample
is different than the standard deviation of the population.
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Cheers,
Stan H.
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