Question

You are obsessed with how many views your pictures get. On average, you get 3022 views per post and always post exactly one picture per day. You’d like to have a month with 100000 or more total views. Find the approximate probability of this occurring in January if we assume view counts from day-to-day are independent.

Answer 1

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