Question (16 marks) a Among the 18 districts in Country A, four, five and nine a
ID: 2936533 • Letter: Q
Question
Question (16 marks)
a Among the 18 districts in Country A, four, five and nine are located in King Island, Queenland and the Prince Territories respectively. Suppose that five districts are to be randomly selected. i If the selection is with replacement, what is the probability that exactly three of them will be from the Prince Territories? (4 marks)
ii If the selection is without replacement, what is the probability that exactly three of them will be from the Prince Territories’? (3 marks)
b Suppose that phone calls coming in to the enquiry hotline of a telecommunications corporation follow a Poisson distribution with an average rate of three calls per minute. What is the probability that: i exactly two calls will come in during a particular one-minute interval? (4 marks)
ii more than one call will come in during a particular two-minute interval? (5 marks)
Explanation / Answer
Ans:
a)with replacement:
probability that exactly three of them will be from the Prince Territories=9C3*9C2/18C5
=3024/8568
=0.3529
b)without replacement
(9*8*7/18*17*16)*(9*8/15*14)=0.0353
b)mean=3 per min
i)P(x=2)=e-3*(3^2/2!)=0.2240
ii)P(x>1)=1-P(x=0)-P(x=1)
=1-e-6(1+6^1/1!)
=1-e-6*7=1-0.0174=0.9826