A Recent Survey in Victoria Revealed That 60% of the Vehicles

Essay

A recent survey in Victoria revealed that 60% of the vehicles travelling on highways, where speed limits are posted at 100 kilometres per hour, were exceeding the limit. Suppose you randomly record the speeds of 10 vehicles travelling on the Hume Highway, where the speed limit is 100 kilometres per hour. Let X denote the number of vehicles that were exceeding the limit. Find the following probabilities.
a. P(X = 10).
b. P(4 < X < 9).
c. P(X = 2).
d. P(3 $\le$ X $\le$ 6).