<p>GDC Method:</p>
<ol class="num-list"><li><div class="list-item-content"><span class="list-item-text">The GDC has a function called "Inverse Binomial \(N\)" where it returns the answer for total number of trials \(n\), when the following are given:</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Probability of success: \(p\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">Cumulative probability \(\mathrm{P}(X \leq x)\)</span></div></li></ol></li></ol>
<p>In order to rewrite into the format that GDC can solve, we start out with</p>
<p>\[\mathrm{P}(X \geq 1) &gt; 0.95\]</p>
<p>And rewrite into</p>
<p>\[\mathrm{P}(X \leq 0) \leq 0.05\]</p>
<p>*Note that the upper limit must be inclusive in the cumulative probability.</p>
<ol class="num-list" start="2"><li><div class="list-item-paragraph">Open a new 'Calculator' page and go to: menu > 6: Statistics > 5: Distribution > D: Inverse Binomial N...</div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1776415523388-ov9z9551nbo.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="num-list" start="3"><li><div class="list-item-paragraph">Fill in the cumulative probability which is the maximum value of probability allowed, and probability of success p.<br>The successes x is the upper limit of x for the cumulative probability.<br>You may want to click Matrix form, where they show you the two values of n before and after surpassing \(0.05\) the required value. </div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1776415700863-5m9ib5jpvpr.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="num-list" start="4"><li><div class="list-item-paragraph">As shown in the result, when&nbsp;\(n = 8\), \(P(X \leq 0) = 0.0577\) and when&nbsp;\(n = 9\), \P(X \leq 0) = 0.0404\), and so \(n =9\) is the solution.</div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1776415798656-uheisk9hbvq.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

The GDC has a function called "Inverse Binomial \(N\)" where it returns the answer for total number of trials \(n\), when the following are given:

Cumulative probability \(\mathrm{P}(X \leq x)\)

In order to rewrite into the format that GDC can solve, we start out with

*Note that the upper limit must be inclusive in the cumulative probability.

Open a new 'Calculator' page and go to: menu > 6: Statistics > 5: Distribution > D: Inverse Binomial N...

Fill in the cumulative probability which is the maximum value of probability allowed, and probability of success p.
The successes x is the upper limit of x for the cumulative probability.
You may want to click Matrix form, where they show you the two values of n before and after surpassing \(0.05\) the required value. 

As shown in the result, when \(n = 8\), \(P(X \leq 0) = 0.0577\) and when \(n = 9\), \P(X \leq 0) = 0.0404\), and so \(n =9\) is the solution.

Using GDC to solve problems

Using GDC to solve problems