An air flight capacity is 150 passengers. A passenger with a ticket arrives with

Question

An air flight capacity is 150 passengers. A passenger with a ticket arrives with probability 0.95. Assuming that passenger behave independently of each other,

a) find the minimum number of tickets that should be sold so that the probability of a full flight is at least 0.90;

b) find the maximum number of tickets that can be sold so that the probability that the number of arriving passengers exceeds the flight capacity is no more than 0.10.

4. Let X be the random variable with the following probability mass function: f(5) 0.1, f(10) = 0.2, f(15) 0.3 and f(20) = 0.4. Let F(x) be the cumulative distribution function of X. Find the following quantities. a) F(17) b) P(4s X 10) d) E(X) e) E(X2) f) V(x)

Explanation / Answer

Ans:

Let x be the number of passenger who arrives for flight.

Then x has binomial distribution with p=0.95 and n is unknown.

a)P(flight is full)=P(x>=150)>=0.9

1-P(x<=149)>=0.9

So,n>=162

b)P(overbooked)=P(x>150)<=0.1

1-P(x<=150)<=0.1

So,n<=154

n 1-P(x<=149) 150 0.0005 151 0.0039 152 0.0168 153 0.0494 154 0.1119 155 0.2082 156 0.3325 157 0.4710 158 0.6069 159 0.7262 160 0.8210 161 0.8900 162 0.9363

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