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Question 8 A collar manufacturer is considering the production of new collars to attract young men. Thus following statistics of neck circumference are available based on measurements of a typical group of students of a particular university: \begin{tabular}{l|c|c|c|c|c|c|c|c|c} \hline Mid values (in inches): & 13.0 & 13.5 & 14.0 & 14.5 & 15.0 & 15.5 & 16.0 & 16.5 & 17.0 \\ \hline Number of students: & 2 & 16 & 36 & 60 & 76 & 37 & 18 & 3 & 2 \\ \hline \end{tabular} Compute the standard deviation and use the criterion $\overline{\boldsymbol{x}} \pm \mathbf{3} \sigma$, where $\sigma$ is the standard deviation and $\bar{x}$ is the arithmatic mean to determine the largest and smallest size of the collar he should make in order to meet the needs of practically all the customers, bearing in mind that collars are worn average half an inch longer than the neck size.

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