CourseCourseConceptConceptDocsDocuments

AP Statistics 2.9 B Interpret the Mean and Standard Deviation for a Discrete Random Variable Questions

Practise interpreting expected value as a long-run average, standard deviation as typical distance from the mean, and conditioning as a change to the distribution.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • interpret expected value as the average outcome per repetition over many repetitions of the random process
  • interpret standard deviation as the typical distance of a random-variable value from its mean in context
  • explain how conditioning away low or high outcomes changes the probabilities and therefore the expected value

AP Statistics 2.9 B Interpret the Mean and Standard Deviation for a Discrete Random Variable Questions question 1

A shopping mall has three automated teller machines (ATMs). Because the machines receive heavy use, they sometimes stop 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 AP Statistics 2.9 B Interpret the Mean and Standard Deviation for a Discrete Random Variable Questions 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.

All question bank results loaded