Answer to Question #173283 in Statistics and Probability for Denisse Bisuña

Question

A molding machine prepares a certain kind of car spare part with a target diameter μ = 40.265 millimeters. The machine has some variability so the standard deviation of the diameters is σ = 0.004 millimeters. A sample of 6 spare parts is inspected each hour for process control purposes and records are kept of the sample mean diameter. What will be the mean and standard deviation of the numbers recorded?

Answer 1

Let $X_1, X_2, ..., X_6$ be a random sample from a normal distribution with mean $\mu$ and standard deviation $\sigma.$ Then by the Central Limit Theorem $\bar{x}$ is normally distributed with mean $\mu$ and standard deviation $\sigma/\sqrt{n}.$

$$mean=40.265\ mm$$

$$standard\ deviation=0.004\ mm/\sqrt{6}=0.0016\ mm$$

If the distribution of a target diameter is not normal, we cannot determine the mean and standard deviation of the numbers recorded.