(See Solution) A recent survey in Victoria revealed that 60% of the vehicles travelling on highways, where the speed limits are posted as 100 kilometres
Question: A recent survey in Victoria revealed that 60% of the vehicles travelling on highways, where the speed limits are posted as 100 kilometres per hour, were exceeding the limit. Suppose the speeds of 10 randomly selected vehicles travelling on the Hume Highway were recorded near the posting "100 kilometres per hour". Let X denote the number of vehicles that was exceeding the limit. Stating the distribution the variable X follows and its parameters, find the following probabilities giving answer correct to 4 decimal places.
- P(X = 10).
- P(4 < X < 9).
- P(X = 2).
- P(3 ≤ X ≤ 6).
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