Question

The average number of passengers arriving at the Bus Station in Lancaster on Tuesday between 8:00 and 9:00 is 900.

1.To model this random phenomenon, which probability distribution is most suitable? Assume that passengers arrive at random at a constant rate throughout the hour.

2.Using the most suitable probability distribution, consider the following three statements:

I. There are 15 passengers arriving every minute on average

II. The standard deviation of the number of passengers arriving in an hour is 30

III. The probability of having 5 or more arrived customers in a period of 10 seconds is 0.11 (rounded to two decimals) Which of the statements I, II, and III are TRUE? explain

Answer #1

1) As the average number of passengers arriving is given for a
fixed interval, **poisson** probability distribution
will be the most suitable to model this phenomenon

2) All the statements I,II and III are TRUE

I) No. of passengers arriving every minute on average = 900/60 = 15

II) For poisson distribution, mean and variance are the same

Thus, standard deviation is equal to square root of mean

Standard deviation of the number of passengers arriving in an hour = √900 = 30

III) Average number of customers who arrive in a period of 10 seconds i.e (1/6) minutes is 15/6 =2.5

Probability of having 5 or more arrived customers = P(X >= 5)

= 1 - P(X < 5)

= 1 - {P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)}

= 1 -

= 1 - 0.8911

= 0.1089 ≈ 0.11

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