Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.9 and a mean diameter of 200 inches.

If 78 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches? Round your answer to four decimal places.

Answer 1

Let X_i ; i=1,2,...,78 denote the mean diameter of the 78 metal shafts sampled. Now each X_i is i.i.d. and

.

Now, let denote the mean diameter of the 78 shafts sampled.

Then,

Now, the probability that the mean diameter of the sampled shafts would differ from the population mean be greater than 0.2 inches is given by:

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