<p style="margin-top: 0.25rem; margin-bottom: 0.5rem">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:</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 100px;"><col style="width: 200px;"><col style="width: 200px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Mean (in hours)</strong></p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Standard deviation (in hours)</strong></p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Durazer</strong></p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$19.87$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.24$</p></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Energi-cell</strong></p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$20.16$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.19$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">$50$ Durazer and $80$ Energi-cell batteries are tested. Determine the distribution of the sample mean exhaustion time 	for each brand. <span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Hence find the probability that the difference in the mean exhaustion times of the two brands of batteries is less than 	$0.2$ hours. <span class="inline-marks">[3]</span></div></li></ol>

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:

<p><strong>Standard deviation (in hours)</strong></p>

$50$ Durazer and $80$ Energi-cell batteries are tested. Determine the distribution of the sample mean exhaustion time 	for each brand. 

Hence find the probability that the difference in the mean exhaustion times of the two brands of batteries is less than 	$0.2$ hours. 

Sampling

International Baccalaureate Higher Level Mathematics

Sampling

Question d61e84fa