Answer:
The approximate probability of getting 100000 views or more in January if we assume view counts from day-to-day are independent = 0.22254
Step-by-step explanation:
January has 31 days.
The average number of views per day = 3022 views per day.
In terms of hourly basis, the average number of views = 3022/24 ≈ 126 views per hour
Then we need to find the probability that the number of views in January is equal to or exceeds 100000.
100000 views in January = 100000/31 = 3225.81 ≈ 3226 views per day
On an hourly basis, 3226 views per day ≈ 135 views per hour.
So, mean = λ = 126 views per hour
x = 135 views per hour.
Using Poisson's distribution function
P(X = x) = (e^-λ)(λˣ)/x!
P(X ≥ x) = Σ (e^-λ)(λˣ)/x! (Summation From x to the end of the distribution)
But it's easier to obtain
P(X < x) = Σ (e^-λ)(λˣ)/x! (Summation From 0 to x)
P(X ≥ x) = 1 - P (X < x)
Putting λ = 126 views/hour and x = 135 views/hour in the Poisson distribution formula calculator
P(X ≥ 135) = 0.22254
