Question

A random sample of five Galaxy 8 smartphones is selected from the production line after final assembly, and the result of the weight control measurement is (in grams) 155.1, 154.8, 155.5, 155.3, and 154.6.What are the average weight, its uncertainty (i.e. the standard deviation of the mean), and the fractional uncertainty? Round the results to a number of significant figures consistent with the precision of the smartphone weight measurements.

Answer 1

Answer with explanation:

Given : A random sample of five Galaxy 8 smartphones is selected from the production line after final assembly, and the result of the weight control measurement is (in grams) are :

X= 155.1, 154.8, 155.5, 155.3, and 154.6.

here, n=5

The average weight :$\overline{x}=\dfrac{\sum^{i=5}_{i=1}x_i}{n}$

$=\dfrac{155.1+154.8+155.5+155.3+154.6}{5}\\\\=\dfrac{775.3}{5}=155.06$

∴ Average weight ($\overline{x}$)=155.06 grams

Uncertainty = Standard deviation: $\sigma=\sqrt{\dfrac{\sum^{i=5}_{i=1}(x_i-\overline{x})^2}{n}}$

$=\sqrt{\dfrac{(0.04)^2+(-0.26)^2+(0.44)^2+(0.24)^2+(-0.46)^2}{5}}$

$=\sqrt{\dfrac{0.532}{5}}=\sqrt{0.1064}=0.326190128606\approx0.33$

i.e. Its uncertainty : $\sigma=0.33$

The fractional uncertainty = $\dfrac{\sigma}{\overline{x}}$

$=\dfrac{0.33}{155.06}=0.00212820843544\approx0.002$