Question

A Sampling of 409 motor Shafts from a very large production Batch shows a sample standard deviation in Diameter of 0.021 mm with a sample mean of 9.251 mm Estimate the mean diameter of the entire batch at a %95 level of confidences?

Answer 1

Answer:

9.248 < $\mu$ < 9.253 mm

Explanation:

Given data:

standard deviation  = 0.021 mm

sample mean = 9.251 mm

total sample = 409 m

confidence interval level = 95%

mean diameter of entire batch  $\mu = \bar X \pm z \frac{\sigma}{\sqrt{n}}$

where

$\bar X$ - sample mean = 9.251 mm

z = critical value

plugginf all value in the above relation to get the mean diameter

$\mu = 9.251 \pm 1.96 \times \frac{0.021}{\sqrt{409}}$

9.248 < $\mu$ < 9.253 mm