Question 1195851
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Historically, 93% of the deliveries of an overnight mail service arrive before 10:30 
the following morning. If a random sample of 500 deliveries is selected, 
what is the probability the sample will have more than 95% of the deliveries arriving 
before 10:30 the following morning?
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            In order for the mathematical and the probabilistic meaning of this problem 

            would become more clear,  let me re-formulate it in this way.



<pre>
                There is a binomial distribution with the individual probability of success of 0.93.

                There is a random sample of 500 trials.

                What is the probability of more than 0.95*500 = 475 successful trials ?



In this formulation, the probability is a standard binomial distribution problem

    P = P(n=500; k>=476; p=0.93).


To facilitate calculations, I use online calculator at this site  https://stattrek.com/online-calculator/binomial.aspx

     It provides nice instructions  and  a convenient input and output for all relevant options/cases.


          The resulting number is P = 0.02796  (rounded).    <U>ANSWER</U>
</pre>

Solved.