What Is the Probability a Moviegoer Waits Less Than 20 Minutes?

[yitriana]

Homework Statement

The manager of a movie theater determines that the average time movie-goers wait in line to buy a ticker for this week's film is 10 minutes, and avg time to wait to buy popcorn is 5 minutes. Assuming waiting times are independent, find probability that moviegoer waits less than 20 minutes before taking his or her seat.

Homework Equations

The Attempt at a Solution

Waiting times for ticket and popcorn can probably be modeled as functions, but I don't know which specific functions. I don't know how to approach the problem

 

[berkeman]

Homework Statement

The manager of a movie theater determines that the average time movie-goers wait in line to buy a ticker for this week's film is 10 minutes, and avg time to wait to buy popcorn is 5 minutes. Assuming waiting times are independent, find probability that moviegoer waits less than 20 minutes before taking his or her seat.

Homework Equations

The Attempt at a Solution

Waiting times for ticket and popcorn can probably be modeled as functions, but I don't know which specific functions. I don't know how to approach the problem

I don't think there's enough information to answer the question. You indeed would seem to need to know the distribution functions, not just the averages. Are you supposed to assume Gaussian distributions maybe?

 

[Mark44]

I agree with berkeman that there isn't enough information given. Assuming that the waiting times are normally distributed, it seems to me that you need to know the standard deviations of the two waiting times in order to calculate any probabilities.

 

[EnumaElish]

The "easy" part: waiting times are usually modeled with the exponential distribution ("E.D."). Question: what is the relationship between the mean and the variance of an E.D.?

The tough part: you have a random variable that is the sum of two exponential variates with distinct parameters. (The wiki page in the link above tells you what to do if their parameters were identical, that is, if lambda1 = lambda2 were the case.) Are you expected to derive this distribution yourself?