Question

87. Airport security The Transportation Security Admini- pg 402 stration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight had 76 passengers-12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. Can we use a binomial distribution to ap- proximate this probability? Justify your answer

Answer 1

87.

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is executed
p = success probability
mean = 76 * 0.1578
= 11.9928
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 76 * 0.1578 * 0.8422
= 10.1003
III.
standard deviation = sqrt( variance ) = sqrt(10.1003)
=3.1781

probability that some passengers were surprised when none of 10 passengers chosen for screening
were seated in first class
P( X = 10 ) = ( 76 10 ) * ( 0.1578^10) * ( 1 - 0.1578 )^66
= 0.1092