Question

The diameter of small bolts manufactured at a factory in China is expected to be approximately
normally distributed with a population mean of 3 inches and a population standard deviation of .3
inches. Calculate a confidence interval which would contain 95% of all possible sample means.
Suppose the mean of the sample of 30 bolts is 3.75 inches. Using the interval that you calculated in
“A”, what would you conclude regarding this sample of bolts?

Answer 1

Here' the answer to the question. Please let me know in case you've questions.

Normal distribution parameters are here:

Mean = 3
stdev = .3

95% CI is given by a Z of 1.96 and the formula of sample Mean +/- Z*stdev/sqrt(n)
= 3.75 +/- 1.96*.3/sqrt(30)
= 3.643 to 3.857

Now, 95% CI is (3.643,3.857)

Conclusion: The interval doesn't have the population sample. hence, this sample of bolts doesn't come from the specified small bolts manufacured at the factory in China