Question 1170778: At a particular hospital, records show that each day, on average, only 80% of people keep
their appointment at the outpatients’ clinic.
Find the probability that on a day when 200 appointments have been booked;
(b) At least 155 patients keep their appointments [3]
Answer by ikleyn(52921)   (Show Source):
You can put this solution on YOUR website! .
At a particular hospital, records show that each day, on average, only 80% of people keep
their appointment at the outpatients’ clinic.
Find the probability that on a day when 200 appointments have been booked;
(b) At least 155 patients keep their appointments [3]
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The original problem is a binomial distribution, but since the number of trials is too great,
we should use the normal distribution approximation.
It has the mean of m = n*p = 200*0.8 = 160 and the standard deviation
SD =  =  = 5.656854249.
Now you can use your regular calculator like TI-83/84.
Use the standard function normcdf (normal cumulative distribution function) in this format
z1 z2 m SD <<<---=== formatting pattern
p = normcdf(154.5, 9999, 160, 5.6568)
Here 154.5 is the continuing approximation to "at least 155".
Alternatively, you may use online free of charge calculator
https://onlinestatbook.com/2/calculators/normal_dist.html
which has very convenient visual interface.
The ANSWER is p = 0.8345.
Solved.
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