When someone buys a ticket for an airline flight there is a

When someone buys a ticket for an airline flight, there is a 0.0987 probability that the person will not show up for the flight. A certain jet can seat 16 passengers. Is it wise to book 18 passengers for a flight on the jet? Explain. Determine whether or not booking 18 passengers for 16 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet. (Round to four decimal places as needed.)

A. It is a wise decision because the probability that there are not enough seats on the jet is __. So, overbooking is not an unlikely event.

B. It is not a wise decision because the probability that there are not enough seats on the jet is __. So, overbooking is an unlikely event.

C. It is a wise decision because the probability that there are not enough seats on the jet is __. So, overbooking is an unlikely event.

D. It is not a wise decision because the probability that there are not enough seats on the jet is __. So, overbooking is not an unlikely event.

Solution

The flight will overbook if at least 17 will show up.

P(show up) = p = 1 - 0.0987 = 0.9013.

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Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    18      
p = the probability of a success =    0.9013      
x = our critical value of successes =    17      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   16   ) =    0.54230764
          
Thus, the probability of at least   17   successes is  
          
P(at least   17   ) =    0.45769236

As this is not a rare event, then

OPTION D:

D. It is not a wise decision because the probability that there are not enough seats on the jet is 0.45769236 [ANSWER]. So, overbooking is not an unlikely event.