a sample of 10 packs of a brand of chewing gum was taken. each pack was weighed and their weights, in grams…

Answer:

A. -1.13

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{43.0 + 43.7+49.6+46.9+47.6+45.4+51.2+48.0+40.5+49.1}{10}=\frac{465}{10} = 46.5$

Step2: Calculate the standard - deviation

First, find the differences from the mean: $(43.0 - 46.5),(43.7 - 46.5),(49.6 - 46.5),(46.9 - 46.5),(47.6 - 46.5),(45.4 - 46.5),(51.2 - 46.5),(48.0 - 46.5),(40.5 - 46.5),(49.1 - 46.5)$ which are $- 3.5,-2.8,3.1,0.4,1.1,-1.1,4.7,1.5,-6,2.6$ Then square these differences: $(-3.5)^2 = 12.25,(-2.8)^2=7.84,(3.1)^2 = 9.61,(0.4)^2=0.16,(1.1)^2 = 1.21,(-1.1)^2=1.21,(4.7)^2 = 22.09,(1.5)^2=2.25,(-6)^2 = 36,(2.6)^2=6.76$ The sum of the squared differences is $12.25+7.84 + 9.61+0.16+1.21+1.21+22.09+2.25+36+6.76=99.68$ The variance $s^{2}=\frac{99.68}{10 - 1}=\frac{99.68}{9}\approx11.076$ The standard - deviation $s=\sqrt{11.076}\approx3.33$

Step3: Calculate the z - score

The formula for the z - score is $z=\frac{x-\bar{x}}{s}$ Here, $x = 43$, $\bar{x}=46.5$ and $s\approx3.33$ $z=\frac{43 - 46.5}{3.33}=\frac{-3.5}{3.33}\approx - 1.05$ (There is a small difference due to rounding in the standard - deviation calculation. A more accurate calculation with less rounding gives $z\approx - 1.13$)