- The amount of time spent waiting in line at a grocery store express checkout varies from 5 minutes to 15 minutes and follows a uniform distribution. Let X be the amount of time spent waiting in line.
f) Suppose you arrive at the express checkout (with less than 8 items, of course) at 5:00 p.m. and have plans to meet a friend at the food court at 5:20 p.m. If it takes 6 minutes for your groceries to be scanned and paid for and 2 minutes to walk from the store to the food court, what is the probability you will be on time to meet your friend?
Since it is uniform I have sketched the graph in my notes and found that the Height of the uniform distribution is 1/10...but I'm not sure what to do next.
Hint: first calculate the net time $t$ you have left for queueing after accounting for the scanning and walking. Then calculate the probability that your actual queueing time $X$ is less than or equal to $t.$