Your company operates a van service from the airport to down

Your company operates a van service from the airport to downtown hotels. Each van carries 7 passengers. Many passengers who reserve seats don’t show up – in fact., the probability is 0.2 that a randomly chosen passenger will fail to appear. Passengers are independent. If you allow 9 reservations for each van, what is the probability that more than 7 passengers will appear? Do a simulation to estimate this probability

Solution

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success = 1 - 0.2 = 0.8      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   7   ) =    0.563792384
          
Thus, the probability of at least   8   successes is  
          
P(more than   7   ) =    0.436207616 [ANSWER]