exercise:Aa6eb5d51f: Difference between revisions

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Two instruments are used to measure the height, <math>h</math>, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056 <math>h </math>. The error made by the more accurate instrument is normally distributed with mean 0 and standard deviation 0.0044 <math>h</math>.
The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is exponentially distributed. An insurance company expects that 30% of high-risk drivers will be involved in an accident during the first 50 days of a calendar year.
The errors from the two instruments are independent of each other.


Calculate the probability that the average value of the two measurements is within 0.005 <math>h</math> of the height of the tower.
Calculate the portion of high-risk drivers are expected to be involved in an accident during the first 80 days of a calendar year.


<ul class="mw-excansopts">
<ul class="mw-excansopts">
<li>0.38</li>
<li>0.15</li>
<li>0.47</li>
<li>0.34</li>
<li>0.68</li>
<li>0.43</li>
<li>0.84</li>
<li>0.57</li>
<li>0.90</li>
<li>0.66</li>
</ul>
</ul>


{{soacopyright | 2023}}
{{soacopyright | 2023 }}

Latest revision as of 13:13, 2 May 2023

The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is exponentially distributed. An insurance company expects that 30% of high-risk drivers will be involved in an accident during the first 50 days of a calendar year.

Calculate the portion of high-risk drivers are expected to be involved in an accident during the first 80 days of a calendar year.

  • 0.15
  • 0.34
  • 0.43
  • 0.57
  • 0.66

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.