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.1A.] What is the mean and standard deviation for these six samples?2A.] What number of errors is made by all scans, based on these six samples?Just to be sure, the manager has six more samples taken: 33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each1B.] How do the mean and standard deviation change, based on all 12 samples?2B.] How reasonable is it to expect that the small sample represents larger samples?

Accepted Solution

Answer:1A. 20.52A. 14.541B. 14.6252B. quite good reasonableStep-by-step explanation:Mean is used to measure central tendency (i.e. representative of data) and standard deviation is use to measure dispersion of data. The formula use to calculate mean and variance is : [tex]Mean(bar{x}) = \dfrac{Sum of all the observations}{Total number of observation}[/tex][tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_{i}-\bar{x})^2}[/tex]1A. Mean of six sample = [tex]= \dfrac{Sum of all the observations}{Total number of observation}[/tex]⇒ [tex]\dfrac{36+14+21+39+11+2}{6}[/tex]⇒ Mean = 20.5Standard deviation of six sample = [tex] = \sqrt{\frac{1}{6}[ (36-20.5)^2+(14-20.5)^2+(21-20.5)^2+(39-20.5)^2+(11-20.5)^2+(2-20.5)^2}][/tex]⇒ σ = 14.542A. Total number of error = 36 + 14 + 21 + 39 + 11 + 2 = 123Total number of error made by all scans is 123 error per 6000 scans.1B. Mean of all 12 samples is:[tex]= \dfrac{Sum of all the observations}{Total number of observation}[/tex]⇒ [tex]\dfrac{36+14+21+39+11+2+33+45+34+17+1+29}{12}[/tex]⇒ Mean = 23.5Standard deviation of all 12 samples = [tex] = \sqrt{\frac{1}{12}[ (36-23.5)^2+(14-23.5)^2+(21-23.5)^2+(39-23.5)^2+(11-23.5)^2+(2-23.5)^2+(33-23.5)^2+(45-23.5)^2+(34-23.5)^2+(17-23.5)^2+(1-23.5)^2+(29-23.5)^2}][/tex]⇒ σ = 14.6252B. Taking small sample instead of large sample can be quite risky sometimes as larger sample give us more accurate result than small sample.But here we can take a small sample because the mean of both the size of the sample is near about.