The exhaustion time of an alkaline battery is defined as the time it takes to discharge completely u

Question

The exhaustion time of an alkaline battery is defined as the time it takes to discharge completely under controlled experimental conditions. Research has shown that the exhaustion time of AA-size alkaline batteries manufactured by the market leaders, Durazer and Energi-cell, have the following population parameters:

	Mean (in hours)	Standard deviation (in hours)
Durazer	$19.87$	$0.24$
Energi-cell	$20.16$	$0.19$

$50$ Durazer and $80$ Energi-cell batteries are tested. Determine the distribution of the sample mean exhaustion time for each brand. [2]
Hence find the probability that the difference in the mean exhaustion times of the two brands of batteries is less than $0.2$ hours. [3]

Accepted Answer

(i) $\bar D\mathrel{\dot\sim}N\left(19.87,\frac{0.24^2}{50}\right)$, $\bar G\mathrel{\dot\sim}N\left(20.16,\frac{0.19^2}{80}\right)$ (ii) $0.0123\text{ (3 s.f.)}$

Sampling - Central Limit Theorem

Sampling - Central Limit Theorem

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Solution:

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	Mean (in hours)	Standard deviation (in hours)
Durazer	\(19.87\)	\(0.24\)
Energi-cell	\(20.16\)	\(0.19\)