Let x 1 , x 2 , . . . , x 100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with...


Letx
1,x
2, . . . ,x
100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 75 lbs and variance 1 lb2. Let x be the sample mean weight
(n = 100).




(a)


Describe the sampling distribution of x.


The distribution is approximately normal with a mean of 75 lbs and variance of 1 lb2.The distribution is approximately normal with a mean of 75 lbs and variance of 0.01 lbs2.     The distribution is unknown with a mean of 75 lbs and variance of 0.01 lbs2.The distribution is unknown with a mean of 75 lbs and variance of 1 lb2.The distribution is unknown with unknown mean and variance.





(b)


What is the probability that the sample mean is between 74.65 lbs and 75.35 lbs? (Round your answer to four decimal places.)


P(74.65 ≤ x ≤ 75.35) =




(c)


What is the probability that the sample mean is greater than 75 lbs?





Jun 10, 2022
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