<p>A survey is conducted in a large office building. It is found that $30%$ of the office workers weigh less than $62$ kg and that $25\%$ of the office workers weigh more than $98$ kg. The weights of the office workers may be modelled by a normal distribution with mean $\mu $ and standard deviation $\sigma $.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">Detemine two simulatneous linear equations satisfied by $\mu $ and $\sigma $.</div></li><li><div class="list-item-paragraph">Find the values of $\mu $ and $\sigma $.<span class="inline-marks">[6]</span></div></li></ol></li><li><div class="list-item-paragraph">Find the probability that an office worker weighs more than $100$ kg. 	<span class="inline-marks">[1]</span></div></li></ol>
<p>There are elevators in the office building that take the office workers to their offices.

</p>
<p>Given that there are $10$ workers in a particular elevator,</p>
<ol class="abc-list" start="3"><li><div class="list-item-paragraph">find the probability that at least four of the workers weigh more than $100$ kg.	<span class="inline-marks">[2]</span></div></li></ol>
<p>Given that there are $10$ workers in an elevator and at least one weight more than $100$ kg,</p>
<ol class="abc-list" start="4"><li><div class="list-item-paragraph">find the probability that there are fewer than four workers exceeding $100$ kg.	<span class="inline-marks">[3]</span></div></li></ol>

A survey is conducted in a large office building. It is found that $30%$ of the office workers weigh less than $62$ kg and that $25\%$ of the office workers weigh more than $98$ kg. The weights of the office workers may be modelled by a normal distribution with mean $\mu $ and standard deviation $\sigma $.

Find the probability that an office worker weighs more than $100$ kg. 	

There are elevators in the office building that take the office workers to their offices.



Given that there are $10$ workers in a particular elevator,

find the probability that at least four of the workers weigh more than $100$ kg.	

Given that there are $10$ workers in an elevator and at least one weight more than $100$ kg,

find the probability that there are fewer than four workers exceeding $100$ kg.	

Normal Distribution

International Baccalaureate Higher Level Mathematics

Linear Combinations, Probability Modeling, and Parameter Estimation

Linear Combinations, Probability Modeling, and Parameter Estimation