Answer to Question #343933 in Statistics and Probability for bel

Question

 A hardware manufacturer produces bolts used to assemble various machines. Assume that the diameter of bolts produced by this manufacturer has an unknown population mean 𝝁 and the standard deviation is 0.1 mm. suppose the average diameter of a simple random sample of 50 bolts is 5.11 mm. (a) Calculate the margin of error of a 95% confidence interval for 𝝁.

Answer 1

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} = 1.96.$

$$ME=z_c\times\dfrac{\sigma}{\sqrt{n}}=1.96\times\dfrac{0.1}{\sqrt{50}}$$ $$=0.0277$$