AP Statistics 2.9: Interpreting Discrete Variables
Interpret the mean as a long-run average and the standard deviation as typical distance from that mean for a discrete random variable.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
Interpret the mean as a long-run average and the standard deviation as typical distance from that mean for a discrete random variable.
A shopping mall has three automated teller machines (ATMs). Because the machines receive heavy use, they sometimes working and need to be repaired. Let the random variable X represent the number of ATMs that are working when the mall opens on a randomly selected day. The table shows the probability distribution of X.

Given that at least one ATM is working when the mall opens, would the expected value of the number of ATMs that are working be less than, equal to, or greater than the expected value from part (b) ? Explain.
Part (d):
Given that at least one ATM is working when the mall opens, the expected value of the number of working ATMs would be greater than the expected value calculated in part (b). By eliminating the possibility of 0 working ATMs, the probabilities for 1, 2, and 3 working ATMs all increase proportionally, so the expected value must increase.