Question

An airplane has a front nad a rear door that are bother openedto allow passengers to exit when the plane lands. the planehas 100 passengers seated. the number of passengers exitingthrought the front door shougl have

a) a binomial distribution with mean 50
b) a binomial distribution with 100 trials but successprobability not equal to .5
c)a normal didtribution with a standard deviation of5
d) none of the above

Answer 1

a) a binomial distribution with mean 50

Explanation:

Given that an airplane has a front nad a rear door that are bother opened to allow passengers to exit when the plane lands. the plane has 100 passengers.

These 100 passengers can select either back door or front door with equal probability (assuming)

so probability for selecting front door = 0.5

No of passengers =100

Each passenger is independent of the other

Hence X no of passengers exiting through the front door is binomial with

p =0.5 and n =100

Mean of the variable X = np = 100(0.5) = 50

Variance of X = 100(0.5)(0.5)

Hence std dev = 10(0.5) = 5

So correct answers are

a) a binomial distribution with mean 50