Question

Suppose the number of hits a webpage receives follows a Poisson distribution. The average number of hits per minute is 2.4.

Answer 1

Answer: a) P(x=0) = 0.0907, b) P(x≥10) = 0.7986

Step-by-step explanation: the probability mass function of a possion probability distribution is given as

P(x=r) = (e^-λ)×(λ^r) /r!

Where λ = fixed rate at which the event is occurring and each event is independent of each other = 2.4

a) P(x= at least one) = P(x≥1)

P(x≥1) = 1 - P(x<1)

But P(x<1) = P(x=0) { we can not continue to negative values because our values of x can only take positive values of integer}

Hence, P(x≥1) = 1 - P(x=0)

P(x=0) = e^-2.4 * 2.4^0/(0!)

P(x=0) = 0.0907×1/1

P(x=0) = 0.0907

b) if the average number of hits in 1 minutes is 2.4 then for 5 minutes we have 2.4×5 = 12.

Hence λ = 12.

P(x= at least 10) =P(x≥10) = 1 - P(x≤9)

P(x≤9) will be gotten using a cumulative possion probability distribution table whose area is to the left of the distribution.

From the table P(x≤9) = 0.2014.

P(x≥10) = 1 - 0.20140

P(x≥10) = 0.7986