Question 1201963
.
In a certain book, the frequency distribution of the number of words per page 
may be taken as approximately normal with mean 800 and standard deviation 50. 
If three pages are chosen at random, what is the probability that none of them 
has between 830 and 845 words each?
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                    Step by step



<pre>
(1) the probability that in some page the number of words is between 830 and 845 is

        P = normalcdf(830, 845, 800, 50) = 0.0902

    (using regular calculator TI-83 or TI84 with the standard function normalcdf).



(2)  Hence, the probability that in some page the number of words is NOT between 830 and 845 is

     the complement to it  P' = 1 - 0.0902 = 0.9098.



(3)  And finally, the <U>ANSWER</U> to the problem's question is  {{{0.9098^3}}} = 0.7531  (rounded).
</pre>

Solved, with explanations.



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In his post, &nbsp;@Theo gives different answer from my number.  &nbsp;&nbsp;Why ?


The cause is that &nbsp;@Theo incorrectly treats the problem.


In his solution, &nbsp;he said  &nbsp;" since you are looking for the mean of a sample . . . ".


It is the &nbsp;@Theo's &nbsp;error. &nbsp;In this problem, &nbsp;we &nbsp;ARE &nbsp;NOT &nbsp;looking for the mean of a sample.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The problem's question &nbsp;DOES &nbsp;NOT &nbsp;ask &nbsp;about mean of a sample.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It asks about something totally different.