Q3. (a) The number of knots in a particular type of wood has a Poisson distribution...

Q3.

(a) The number of knots in a particular type of wood has a Poisson distribution with an average of 1.5 knots in 0.28m3 of the wood. Find the probability that a 0.28m3 block of the wood has at most 1 knot. [3]

(b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during the call? [5]

(c) The number of typing errors made by a typist has a Poisson distribution with an average of four errors per page. If more than four errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped? [3]

(d) A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately five per square metre. If a forester randomly locates ten 1-square-metre sampling regions in the area, find the probability that none of the regions will contain seedlings. [5]

Expert Solution

orchestra answered 1 year ago

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