Question

The manager of a warehouse would like to know how many errors are made when a product's serial number is read by a bar-code reader. Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.

Answer 1

Answer:

$(a)\ \bar x =20.5$

$(b)\ \sigma = 14.54$

Step-by-step explanation:

Given

$x: 36, 14, 21, 39, 11, 2$

Solving (a): The mean of the 6 samples.

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x =\frac{36+ 14+ 21+ 39+ 11+ 2}{6}$

$\bar x =\frac{123}{6}$

$\bar x =20.5$

Solving (b): The sample standard deviation.

This is calculated using:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

So, we have:

$\sigma = \sqrt{\frac{(36 - 20.5)^2 + (14 - 20.5)^2 + (21 - 20.5)^2 + (39 - 20.5)^2 + (11 - 20.5)^2 + (2 - 20.5)^2}{6-1}}$

$\sigma = \sqrt{\frac{1057.5}{5}}$

$\sigma = \sqrt{211.5}$

$\sigma = 14.54$