Question

The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3

51.2 44.2 45.4 49.2 43.6

(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.

Answer 1

Answer:

$\mu = 47.17$

$\sigma = 2.31$

Step-by-step explanation:

Solving (a): The population mean

This is calculated as:

$\mu = \frac{\sum x}{n}$

So, we have:

$\mu = \frac{48.2+ 47.8 +45.6 +47.2 +49.3+51.2 +44.2 +45.4 +49.2 +43.6}{10}$

$\mu = \frac{471.7}{10}$

$\mu = 47.17$

Solving (b): The population standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}$

So, we have:

$\sigma = \sqrt{\frac{(48.2-47.17)^2 + (47.8-47.17)^2 +.........+(43.6-47.17)^2}{10}}$

$\sigma = \sqrt{\frac{53.521}{10}}$

$\sigma = \sqrt{5.3521$

$\sigma = 2.31$