An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0.90. If the airline sells 105 tickets, what is the probability that everyone who appears for the flight will get a seat?
What will be an ideal response?
Let X be the number of people out of 105 who appear for the flight.
Then X ~ Bin (105, 0.9), so X is approximately normal with mean 
= 105(0.9)=94.5 and standard deviation 
To find P (X ? 100), use the continuity correction and find the z-score for 100.5.
The z-score of 100.5 is (100.5 ? 94.5) / 3.0741 = 1.95.
The area to the left of z = 1.95 is 0.9744.
P (X ? 100) = 0.9744.
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