<p>The waiting time, \(T\) minutes, of patients at a clinic can be modelled by a  normal distribution with mean \(\mu\) and standard deviation \(\sigma\). The waiting times of all patients are independent of each other.</p>
<p>\( 3.8\%\) of the patients have a waiting time of less than \(20\) minutes, while \(7.3\%\) of the patients have a waiting time of more than \(30\) minutes.</p>
<ol class="abc-list"><li data-list-item-id="item-1788756493789-1pu004jg1" data-list-item-path="item-1788756493789-1pu004jg1"><div class="list-item-paragraph"><span class="inline-marks">[7]</span></div><ol class="i-list"><li data-list-item-id="subitem-1788756495038-8tuq2tzq7" data-list-item-path="item-1788756493789-1pu004jg1/subitem-1788756495038-8tuq2tzq7"><div class="list-item-paragraph"><p>Find the value of \(\mu\) and the value of \(\sigma\).</p></div></li><li data-list-item-id="subitem-1788756495525-jp77zqu8v" data-list-item-path="item-1788756493789-1pu004jg1/subitem-1788756495525-jp77zqu8v"><div class="list-item-paragraph"><p>Hence, find the probability that a patient chosen at random has a waiting time of between \(15\) and \(23\) minutes.</p></div></li></ol></li></ol>
<p>The doctor at the clinic only sees patients with an appointment.<br>Records show that&nbsp;\(82.6\%\) of patients attend their appointment.<br>The probability of a patient attending their appointment is independent of any other patient.</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-1788756646816-u8k42vpsl" data-list-item-path="item-1788756646816-u8k42vpsl"><div class="list-item-paragraph"><p>On a particular day, \(20\) patients each made an appointment to see the doctor.</p><span class="inline-marks">[7]</span></div><ol class="i-list"><li data-list-item-id="subitem-1788756655313-erphgmw7q" data-list-item-path="item-1788756646816-u8k42vpsl/subitem-1788756655313-erphgmw7q"><div class="list-item-paragraph"><p>Find the probability that at least \(13\) of these patients attended their appointment.</p></div></li><li data-list-item-id="subitem-1788756655704-20o8phj0g" data-list-item-path="item-1788756646816-u8k42vpsl/subitem-1788756655704-20o8phj0g"><div class="list-item-paragraph"><p>Given that at least \(13\) of these patients attended their appointment, find the probability that more than \(2\) patients did not attend their appointment.</p></div></li></ol></li></ol>

The waiting time, \(T\) minutes, of patients at a clinic can be modelled by a  normal distribution with mean \(\mu\) and standard deviation \(\sigma\). The waiting times of all patients are independent of each other.

\( 3.8\%\) of the patients have a waiting time of less than \(20\) minutes, while \(7.3\%\) of the patients have a waiting time of more than \(30\) minutes.

The doctor at the clinic only sees patients with an appointment.
Records show that \(82.6\%\) of patients attend their appointment.
The probability of a patient attending their appointment is independent of any other patient.

<p>On a particular day, \(20\) patients each made an appointment to see the doctor.</p>

Binomial Distribution

International Baccalaureate Mathematics: Applications and Interpretation Standard Level