You drive to school 5 days a week for a full year (50 weeks), and with probability p = 0.02 you get a traffic ticket on any given day, independent of other days. Let X be the total number of tickets you get in the year.

Suppose you do not know the probability p of getting a ticket, but you got 5 tickets during the year, and you estimate p by the sample mean: p' = 5 / 5 50 = 0.02. What is the range of possible values of p that are within 5 times the standard deviation of the sample mean (i.e., |p p'| is no greater than 5 times the standard deviation of p')?