Question

You’ve become an influencer and 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

here expected number of views in 31 days of Jan =31*3022=93682

for Poisson distribution ; standard deviation =√mean =√93682 =306.075

since sample size is large(n>30) , we can approximate this with normal distribution:

for normal distribution z score =(X-μ)/σx
here mean=       μ=	93682
std deviation   =σ=	306.075

probability =P(X>100000)=P(Z>(100000-93682)/306.075)=P(Z>20.64)=1-P(Z<20.64)=1-(~1)=~0.0000

the probability of above event happening is almost negligible.