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Savatey [412]
3 years ago
10

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 read

er. Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.
Mathematics
1 answer:
Bond [772]3 years ago
7 0

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

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