AP Statistics 2.9: Mean and Standard Deviation

Calculate the expected value and standard deviation of a discrete random variable from its possible values and associated probabilities.

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

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

A.

What is the mean number of bedrooms for the sample of newly built houses in 2024?

Show your work.

Model Solution
$\begin{aligned} E(X)&=1(0.12)+2(0.22)+3(0.28)\\ &\quad+4(0.22)+5(0.14)+6(0.02)\\ &=3.10\text{ bedrooms}. \end{aligned}$

Scoring components
3. Calculates the mean 3.10.
4. Shows supporting work or justification.

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2.9.A—Calculate the mean and standard deviation for a discrete random variable question 1