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

A normal distribution has mean $100$ and standard deviation $15$ . What value is 1 standard deviation above the mean?

$100 + 1\times15 = 115$ .

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

A normal distribution has mean $50$ and standard deviation $5$ . What value is 2 standard deviation below the mean?

$50 - 2\times5 = 40$ .

Practice playeasy

A ball is tossed upward from a platform. The equation $h = -4.9t^2 + 14t + 21$ represents this situation, where $h$ is the height of the ball above the ground, in meters, $t$ seconds after it is tossed. According to the equation, what is the height, in meters, of the platform from which the ball was tossed?

At the moment of release, $t = 0$ . Substituting gives $h = -4.9(0)^2 + 14(0) + 21 = 21$ meters.

Practice playeasy

The letters of the word BANANA are placed in a bag. Two letters are selected one at a time without replacement. What is the probability of drawing an A and then an N?

The word BANANA has $6$ letters with $3$ A's and $2$ N's. $P(\text{A first}) = \dfrac{3}{6}$ and $P(\text{N second} \mid \text{A first}) = \dfrac{2}{5}$ , so $P(\text{A then N}) = \dfrac{3}{6} \times \dfrac{2}{5} = \dfrac{1}{5}\textsf{.}$