Question 1206486
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Jim is the team statistician. Based on the team's record so far, Jim estimates the probability 
of winning any given game is 0.54. Use a normal approximation to estimate the probability 
the team will win at least 16 of the season's scheduled 31 games.
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<pre>
The oroginal experiment is a Binomial, but we have an instruction to use a normal distribution
as an approximation.


So, for the normal distribution we use the mean m = n*p = 0.54*31 = 16.74
and the standard deviation SD = {{{sqrt(n*p*(1-p))}}} = {{{sqrt(31*0.54*(1-0.54))}}} = 2.775 (rounded).


After that, we calculate the estimate normal probability, using the standard function normcdf 
of the regular calculator TI-83/84

                 z1   z2   mean    SD              <<<---=== formatting pattern
    P = normcdf(15.5,9999, 16.74, 2.775) = 0.6725.


Here the value 15.5 is the continuing correction factor, which serves as approximation for "at least 16".


<U>ANSWER</U>.  The estimated probability is 0.6725.
</pre>

Solved.