SOL Algebra II Statistics and Probability Practice

Statistics and Probability skills

conditional probability

normal distributions

inference and regression

two-way tables and correlations

Standards basis

Virginia Mathematics Standards of Learning — Virginia

How the SOL reports it

Virginia SOL math is a state-specific assessment program built around the Virginia Mathematics Standards of Learning rather than a shared national test framework. It is aligned to Virginia grade-level and course standards, which are generally CCSS-like in organization but are published as Virginia-specific standards.

Blueprint & weighting

SOL uses the Independent / state-specific framework (by grade domains structure).

Official sources

Virginia Department of Education
VDOE — Standards of Learning for Mathematics (2023 SOL grade/course standards and assessment blueprints)
VDOE — SOL Test Blueprints (per-reporting-category item counts live inside the individual grade/EOC blueprint PDFs)

8 free questions · 0/0 correct

Practice playeasy

From a table, 5 are members who renew AND are premium and 12 total are premium members. Find the conditional probability of renewing given premium (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{5}{12} = \dfrac{5}{12}$ .

Practice playeasy

For a normal distribution, approximately what percent of the data lies within $3$ standard deviations of the mean? Use the empirical rule.

By the empirical rule, about $99.7\%$ of the data lie within $3$ standard deviations of the mean.

Practice playeasy

A fair coin is flipped twice. What is the probability of getting heads on both flips?

Each flip has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The flips are independent, so $\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\textsf{.}$

Practice playeasy

A librarian checked $40$ books selected at random from a collection of $800$ books. She found that $14$ of the books in the sample were fiction. Based on the sample, which of the following is the best estimate of the number of fiction books in the collection?

The sample proportion is $\dfrac{14}{40} = \dfrac{7}{20}$ . The best estimate for the collection is $\dfrac{7}{20} \times 800 = 280$ books.

Practice playeasy

In a class of $20$ students, $12$ students bring lunch from home, and $4$ of those students also bring a reusable water bottle. If a student who brings lunch from home is selected at random, what is the probability that the student also brings a reusable water bottle?

Restrict to the $12$ students who bring lunch from home. $4$ of them also bring a bottle, so $P(\text{bottle} \mid \text{lunch from home}) = \dfrac{4}{12} = \dfrac{1}{3}\textsf{.}$

Practice playeasy

From a table, 10 are customers who buy AND saw the ad and 25 total are customers who saw the ad. Find the conditional probability of buying given saw the ad (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{10}{25} = \dfrac{2}{5}$ .

Practice playeasy

For a normal distribution, approximately what percent of data lies within 3 standard deviations of the mean? (Use the empirical rule; enter the number of percent.)

By the empirical rule, about $99.7\%$ lies within 3 SD of the mean.

Practice playeasy

A standard six-sided die is rolled twice. What is the probability of rolling a $6$ on both rolls?

Each roll has a probability of $1$ out of $6\textsf{,}$ or $\dfrac{1}{6}\textsf{.}$ The rolls are independent, so $\dfrac{1}{6} \times \dfrac{1}{6} = \dfrac{1}{36}\textsf{.}$