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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

2.9.B—Interpret the mean and standard deviation for a discrete random variable question 1

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.

Table for Question 2.9.B—Interpret the mean and standard deviation for a discrete random variable question 1 — AP Statistics

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.

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