Ratios, Rates, Probability & Descriptive Stats

Practice Questions

Level 1: Easy (Foundational)

1. A car travels $180$ km in $3$ hours. Determine its exact average speed in km/h. (SPR)
2. What is $25\%$ of $80$?
   A) $15$
   B) $20$
   C) $25$
   D) $40$
3. The mode of $\{2, 4, 4, 5, 7, 7, 7, 9\}$ is:
   A) $4$
   B) $5$
   C) $7$
   D) $9$

Level 2: Medium (Standard)

1. A phone that cost $\$500$ is on sale for $\$400$. Determine the exact percent decrease.
   A) $20\%$
   B) $25\%$
   C) $30\%$
   D) $40\%$
2. A spinner has $4$ equal sectors: red, blue, green, yellow. Determine the exact probability of NOT landing on red.
   A) $\tfrac{1}{4}$
   B) $\tfrac{1}{2}$
   C) $\tfrac{3}{4}$
   D) $1$
3. A car's fuel efficiency is $12$ km per litre. Determine the exact litres to travel $180$ km. (SPR)
4. The correlation coefficient of a scatterplot is $r = -0.85$. Which best describes the relationship?
   A) Strong positive linear
   B) Strong negative linear
   C) Weak positive linear
   D) No correlation

Level 3: Hard (Advanced)

1. A fair six-sided die is rolled twice. Determine the exact probability that the sum is $7$.
   A) $\tfrac{1}{6}$
   B) $\tfrac{1}{9}$
   C) $\tfrac{5}{36}$
   D) $\tfrac{7}{36}$
2. A discrete random variable $X$ has $P(X=x)=\tfrac{x}{10}$ for $x \in \{1,2,3,4\}$. Determine the exact expected value $E(X)$.
   A) $2.5$
   B) $2.8$
   C) $3.0$
   D) $3.5$
3. A dataset of $100$ values has mean $50$ and standard deviation $6$. Determine the approximate number of values within $\pm 2\sigma$ (empirical rule). (SPR)