The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 and standard deviation 1.5 g. If 50 batches are independently prepared, a) What is the mean and standard deviation of the sampling distribution of the sample means? b) If 50 batches are independently prepared, what is the approximate probability that the sample average amount of impurity is between 3.5 and 3.8? c) Find the 95th %tile of the distribution of X-bar.
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0 g. The standard deviation of the sampling distribution of the sample means is equal to the standard deviation of the population divided by the square root of the sample size. So, the standard deviation of the sampling distribution is 1.5/sqrt(50) = 0.212 g. b) Show more…
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When a batch of a certain chemical product is prepared, the amount of a particular impurity in the batch is a random variable with mean value 4 g and standard deviation 1.5 g. If 50 batches are independently prepared. a) What is the (approximate) probability that the sample average amount of impurity X̄ is between 3.5 and 4.1 g? P(3.5 ≤ X̄ ≤ 4.1) = 0.4576 b) What is the (approximate) probability that the sample average amount of impurity X̄ is between 3.8 and 4 g? P(3.8 ≤ X̄ ≤ 4) = 0.3264
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The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 g and standard deviation 1.5 g. If 100 batches are independently prepared, what is the (approximate) probability that the sample average amount of impurity X is between 3.5 and 3.8 g?
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The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 g and standard deviation 1.5 g. If n = 50 batches are independently prepared, what is the probability that the sample average amount of impurity is between 3.5 and 3.8 g? 0.1736 0.0091 0.1645 0.1827
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