Acme Airlines flies airplanes that seat 100 passengers. From experience, they have determined, on average, 84% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 116 passengers for a flight, what is the probability (rounded to four decimals) that 100 or fewer passengers holding reservations will actually show up for the flight?
a. 0.8400
b. 0.8590
c. 0.8621
d. 0.7774
e. 0.7241
okay so when I plug in the numbers into the binomial probability calculator I know that the answer is D. Which makes it p(x≤100) = 0.77738 = 0.7774
But When I try to use p(x)=n!/(n-x)!x!*(p)x (q)n-x I end up with 0.85866 which = 0.8590 So I am not sure if I should be using the Cumulative Binomial Probability Calculator or the equation by hand?
I know that .84 is my probability of successes, 100 is my successes and 116 would be considered my trials.
