<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Steven, who loves soccer, trains his shooting skills by trying to kick balls into the net from distances varying from $15$ metres to $35$ metres. The probability, $p$, that he kicks the ball into the net is given by $p=\frac{2}{65}\left( 40-d \right)$, where $d$ is the distance between the ball and the goalpost in metres.<br>Each kick by him is assumed to be independent of previous kicks.</div><ol class="i-list"><li><div class="list-item-paragraph">Find the maximum value of $d$ (to the nearest integer) for there to be more than $60\%$ chance of Steven kicking the ball into the net.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Steven kicks $15$ balls from a fixed distance of $x$ metres from the goalpost. <br>Find, to the nearest integer, the value of $x$ such that Steven has $90\%$ chance of kicking at least two balls into the net.<br><span class="inline-marks">[4]</span></div></li></ol></li></ol>

Find the maximum value of $d$ (to the nearest integer) for there to be more than $60$% chance of Steven kicking the ball into the net.

Steven, who loves soccer, trains his shooting skills by trying to kick balls into the net from distances varying from $15$ metres to $35$ metres. The probability, $p$, that he kicks the ball into the net is given by $p=\frac{2}{65}\left( 40-d \right)$, where $d$ is the distance between the ball and the goalpost in metres.
Each kick by him is assumed to be independent of previous kicks.

2015 AJC P2 Q11

2015 AJC P2 Q11