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

a. What is the probability the page will get at least one hit during any given minute? (Answer correct to four decimal places.)

b. In the next five minutes, what is the probability the webpage gets at least 10 hits?

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