title: How to find the probability that a standard error is with in a specific amount for a normal distribution?
body: <p>I am trying to find the CLT(Central Limit Theorem) approximation that the probability of the standard error is equal or larger than 0.01 for a normal distribution?</p>
  <p>To calculate the probability that the error is 0.01 or larger</p>
  <p>Given:</p>
  <p>N= Number of samples is 100</p>
  <p>X = The sample average is 0.51</p>
  <p>SE = I calculated the standard error by sqrt(X * (1-X)/N)</p>
  <p>Then I used the <code>pnorm()</code> function.  Please see the code below. When I run the compiler, it gives me an argument error for the <code>pnorm()</code> function.</p>
  <h1>R code</h1>
  <pre><code># `N` is the number of people polled
  N &lt;-100
  
  # `X` is the sample average
  X &lt;- 0.51
  
  # `se` is the standard error of the sample average
  se &lt;- sqrt(X*(1-X)/N)
  
  # Calculating the probability that the error is 0.01 or larger
  1-(pnorm(0.01/se) - pnorm(-0.01/se))
  </code></pre>
  <p>When I run the code, the compiler gives me an argument error for the <code>pnorm()</code> function.</p>