SOLUTION: Random samples of three are drawn from a population of beetles whose lengths have a normal distribution with mean 2.4 cm and standard deviation 0.36 cm.the mean length is calculate

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Question 1172473: Random samples of three are drawn from a population of beetles whose lengths have a normal distribution with mean 2.4 cm and standard deviation 0.36 cm.the mean length is calculated for each sample.
A-State the distribution of X^- giving the value of its parameters.
B-find p(X^- >2.5)
State which of the numerical value above if any depend on the central limit theorem.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sample distribution N~(2.4, 0.0432) or mean 2.4 and sd 0.21; the variance is sigma^2/n
probability X^> 2.5 is z > (2.5-2.4)/0.21 or
z > 0.476
which is probability 0.3170. This comes from the table or from the calculator 2ndVARS2normalcdf(0.476,6) or any number greater than 6.
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So long as the population itself is normal, the sampling distribution of samples with size 3 will also have a normal distribution with the above parameters.