Question

a factory manufactures a specific precision part used in smart phones. many machines are needed to mass produce this part and the performance of these machines is measured in defective parts per million (ppm). according to the factory’s documentation, the factory’s machines have a population mean performance of 23 defective ppm with a population standard deviation of 1.9 defective ppm.

a control engineer was brought in to certify that the factory’s documentation is correct. the engineer examined the performance of a sample of 25 of the factory’s machines. the engineer found that the sample mean was 22 defective ppm with a sample standard deviation of 1.8 defective ppm.

fill in the blanks below with the proper notation for the population mean, the population standard deviation, and the sample mean.

population mean: μ = 23 ppm

population standard deviation: select = 1.9 ppm

sample mean: s² = 22 ppm

Explanation:

Step1: Recall Notation for Population Standard Deviation

The population standard deviation is denoted by $\sigma$. The population has a standard deviation of 1.9 ppm, so the notation is $\sigma$.

Step2: Recall Notation for Sample Mean

The sample mean is denoted by $\bar{x}$. The sample has a mean of 22 ppm, so the notation is $\bar{x}$.

Answer:

Population standard deviation: $\boldsymbol{\sigma}$ = 1.9 ppm
Sample mean: $\boldsymbol{\bar{x}}$ = 22 ppm