Middle School Math Quiz: Approximate Probability From Collected Data

What this quiz covers

This quiz focuses on Approximate Probability From Collected Data, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. About 225 defective widgets, though the actual number may vary from this estimate (correct answer)
2. Exactly 225 defective widgets, since $\frac{15}{200} = \frac{225}{3000}$
3. About 180 defective widgets, accounting for improved quality in larger production runs
4. About 270 defective widgets, since defect rates typically increase with production volume

Question 2

1. The theoretical probability is $\frac{52}{80} = \frac{13}{20}$ based on experimental evidence
2. The coin is biased because 52 is significantly different from the expected 40 heads
3. The theoretical probability is still $\frac{1}{2}$, and the experimental result shows natural variation (correct answer)
4. More trials are needed because 80 flips cannot determine theoretical probability accurately

Question 3

1. Exactly 300 bulbs will be defective based on the experimental data
2. Approximately 300 bulbs will be defective, but the actual number will vary (correct answer)
3. Approximately 250 bulbs will be defective, accounting for improved quality over time
4. Between 280 and 320 bulbs will be defective due to statistical variation

Question 4

1. Exactly 96 blue marbles, since the ratio should remain constant
2. About 96 blue marbles, based on the observed relative frequency of blue (correct answer)
3. About 80 blue marbles, since outcomes should balance out over time
4. About 72 blue marbles, proportionally scaling down from the original experiment

Question 5

1. The coin is unfair because 10 flips should give exactly 5 heads.
2. The theoretical probability of heads is now $0.7$ because of these 10 flips.
3. The experimental probability is $\frac{7}{10}=0.7$, but with more flips it may get closer to $0.5$. (correct answer)
4. The coin is guaranteed to land on heads 70% of the time forever.

Question 6

1. About 100 times
2. About 40 times (correct answer)
3. Exactly 40 times every time the experiment is done
4. About 20 times

Question 7

1. Exactly 100 times
2. About 100 times (correct answer)
3. About 200 times
4. About 300 times

Question 8

1. The experimental probability is 47/100=0.47, which is close to 0.5 (correct answer)
2. The probability of heads has changed to exactly 0.47
3. The coin must be unfair because the result is not 50 heads
4. The experimental probability is 53/100=0.53, so it is not close to 0.5

Question 9

1. $\frac{110}{13}\approx 8.46$
2. $\frac{110}{400}=0.275$ (correct answer)
3. $\frac{400}{110}\approx 3.64$
4. $\frac{110}{52}\approx 2.12$

Question 10

1. $0.225$ (correct answer)
2. $0.45$
3. $0.18$
4. $0.80$

Question 11

1. $\frac{18}{120}=0.15$ (correct answer)
2. $\frac{18}{120}=0.018$
3. $\frac{102}{120}=0.85$
4. $\frac{120}{18}\approx 6.67$

Question 12

1. It gets farther from $0.5$ as more flips are done.
2. It becomes exactly $0.5$ every time once you reach 100 flips.
3. It gets closer to $0.5$ as more flips are done. (correct answer)
4. It always stays the same as the result from the first 10 flips.

Question 13

1. $\frac{110}{400}=0.275$ (correct answer)
2. $\frac{400}{110}\approx 3.64$
3. $\frac{110}{13}\approx 8.46$
4. $\frac{110}{52}\approx 2.12$

Question 14

1. The experimental probability of heads is $\frac{60}{100}=0.60$, which is an estimate and may differ from $0.50$ because of randomness. (correct answer)
2. Because 60 is more than 50, the coin must have two heads.
3. If the coin is flipped 100 more times, it will definitely get exactly 40 heads to balance out.
4. The probability of heads is now exactly $0.60$ for this coin.

Question 15

1. The experimental probability is exactly $\frac{1}{4}$ because the spinner is supposed to be fair.
2. Since $\frac{1}{4}$ is the theoretical probability, 58 is impossible in 200 spins.
3. Experimental probability $=\frac{58}{200}=0.29$, which is close to $0.25$ but not exactly the same. (correct answer)
4. Experimental probability $=\frac{200}{58}\approx 3.45$, so it is close to $0.25$.

Question 16

1. About 150 times, since 2 and 5 appeared 100 times total in 300 rolls (correct answer)
2. About 135 times, scaling the combined frequency of 2 and 5 proportionally
3. About 120 times, because experimental results typically decrease with more trials
4. About 180 times, since each outcome should appear equally in larger samples

Question 17

1. The player will make exactly 160 shots, matching the practice success rate exactly.
2. The player will make between 155 and 165 shots, based on typical statistical patterns.
3. The player will make fewer than 160 shots, since game pressure usually lowers performance.
4. The player will make about 160 shots, though some variation from that number is expected. (correct answer)

Question 18

1. About 50 hearts (correct answer)
2. About 25 hearts
3. Exactly 50 hearts
4. About 150 hearts

Question 19

1. 60/21 approx 2.86
2. 39/60=0.65
3. 21/60=0.35 (correct answer)
4. 21/60=0.035

Question 20

1. 80/30 approx 2.67
2. 30/80=0.375 (correct answer)
3. 50/80=0.625
4. 30/80=0.0375