Daily Normal RV
You are drawing from a normally distributed random variable (RV) once a day. What is the approximate expected number of days until you get a value greater than 2?
This is the same question as problem #16 in the Statistics Chapter of Ace the Data Science Interview!
Since is normally distributed, we can employ the cumulative distribution function (CDF) of the normal distribution:
Knowing that X has a standard normal probability distribution, we can use the CDF to find the probability of X being at least 2:
Therefore, for any given day. Since each day's draws are independent, the expected time until drawing an follows a geometric distribution, with . Letting be a random variable denoting the number of days, we have the following: