SOLUTION: 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 whe

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]
~~~~~~~~~~~~~~~~~~~~~~~~

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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