Chapter 11.10, Problem 18PPSE

Solution

To calculate: The probability that a box will not contain between 95 and 105 clips.

The probability that a box will not contain between 95 and 105 clips is 0.32.

Given:The number of paper clips per box follows a normal distribution with mean $\mu =100$ and standard deviation $\sigma =5$ .

Concept used:

The Empirical rule states that within one standard deviation of the mean, there is about 68% of the data, within two standard deviations of the mean, there is about 95% of the data, and within three standard deviations of the mean, there is about 99.7% of the data.

  

Calculation:

With reference to the normal distribution curve and empirical rule as shown above the one standard deviation away from points are calculated as shown below

  $\begin{array}{l}\mu -\sigma =100-5=95\\ \mu +\sigma =100+5=105\end{array}$

Thus according to empirical rule 95 and 105 are one standard deviation away from the mean, thus between them about 68% of the data lie. Thus there is about $(100-68)$ , 32% of the data does not lie between 95 and 105.

Conclusion:With reference to the empirical rule, the probability that a box will not contain between 95 and 105 paper clips is 0.32.