AP Statistics 2.9: Random Variable Parameters
Calculate and interpret the expected value and standard deviation of a discrete random variable from its probability distribution.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
Covered syllabus points
2.9 Parameters of Random Variables question 1
According to a 2017 national survey in Country B, the mean number of bedrooms in newly built
houses was 2.9. Rodney, a researcher, believes the mean number of bedrooms in newly built
houses in the country was different in 2024 than it was in 2017. To investigate his belief, he took
a large random sample of newly built houses in Country B in 2024 and recorded the number of
bedrooms in each house. The distribution of the number of bedrooms for the sampled houses is
summarized in the table.
Distribution of the Number of Bedrooms for the Houses Sampled in 2024
A.
What is the mean number of bedrooms for the sample of newly built houses in 2024?
Show your work.
2.9 Parameters of Random Variables question 2
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.
Question (a)
(a)
What is the expected value of the number of ATMs that are working when the mall opens?
Question (b)
(b)
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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