a) Ahmad has 30 hens. The probability that any hen lays an egg is 0.7. Hens do not lay more than one egg per day, and the days on which a hen lays an egg are independent. a. Calculate the probability that Ahmad's hens lay exactly TWENTY-FOUR (24) eggs. b. Is it possible for Ahmad's hens to lay less than TWO (2) eggs? Justify your answer. b) A plane lands at a constant average rate of one every ten minutes. Find the probability that: - At most THREE (3) planes land in a period of 10 minutes. - At least TWO (2) planes will land in a period of 16 minutes. - Exactly FIVE (5) planes will land in a period of one hour. c) The time taken by a postman to reach Taman Zamrud from the post office is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. He goes to Taman Zamrud every day. Find the probabilities that the postman takes: - Longer than SEVENTEEN (17) minutes. - Less than TEN (10) minutes.
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