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Grade 12 Quiz: Data, Statistics & Probability — Easy Version 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Expected Value & Binomial Probability: A game costs nothing to enter. You win $18 with probability 12; otherwise you lose $2. What is the expected value of the game in dollars? (Use a negative number for an expected loss.)
Answer: 8
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distribution & z-Scores
The z-score z = (x - μ) / σ counts standard deviations from the mean. The 68-95-99.7 rule: about 68% of data lies within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ, so each band holds 34%, 13.5%, 2.35%, and 0.15% on each side.
Try a similar one
The battery lifetimes (hours) are normally distributed with mean 430 and standard deviation 20. Find the z-score of a lifetime of 450.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | 4 | 6 | 7 |
|---|---|---|---|
| P(x) | 0.1 | 0.2 | 0.7 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Expected Value & Binomial Probability
Expected value: E(X) = Σ x·P(x), multiply each outcome by its probability and add. Binomial: with n independent trials and success probability p, P(X = k) = C(n, k)·pk·(1 - p)n-k, and the mean is np.
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The table shows the probability distribution of X. Find the expected value E(X).
| x | 0 | 2 | 9 |
|---|---|---|---|
| P(x) | 0.4 | 0.4 | 0.2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Statistics & Probability
To count ways to choose r items from n, use C(n, r) = n! ÷ (r! × (n - r)!). For independent events, P(A and B) = P(A) × P(B); write the probability as a fraction in simplest form.
Try a similar one
How many ways can you choose 2 items from a set of 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distribution & z-Scores
The z-score z = (x - μ) / σ counts standard deviations from the mean. The 68-95-99.7 rule: about 68% of data lies within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ, so each band holds 34%, 13.5%, 2.35%, and 0.15% on each side.
Try a similar one
The battery lifetimes (hours) are normally distributed with mean 570 and standard deviation 20. Find the z-score of a lifetime of 590.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Expected Value & Binomial Probability
Expected value: E(X) = Σ x·P(x), multiply each outcome by its probability and add. Binomial: with n independent trials and success probability p, P(X = k) = C(n, k)·pk·(1 - p)n-k, and the mean is np.
Try a similar one
The table shows the probability distribution of X. Find the expected value E(X).
| x | 4 | 5 | 10 |
|---|---|---|---|
| P(x) | 0.4 | 0.4 | 0.2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Statistics & Probability
To count ways to choose r items from n, use C(n, r) = n! ÷ (r! × (n - r)!). For independent events, P(A and B) = P(A) × P(B); write the probability as a fraction in simplest form.
Try a similar one
Two 6-sided dice are rolled. What is the probability that both show a 6? (as a fraction)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distribution & z-Scores
The z-score z = (x - μ) / σ counts standard deviations from the mean. The 68-95-99.7 rule: about 68% of data lies within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ, so each band holds 34%, 13.5%, 2.35%, and 0.15% on each side.
Try a similar one
The battery lifetimes (hours) are normally distributed with mean 440 and standard deviation 20. Find the z-score of a lifetime of 420.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Expected Value & Binomial Probability
Expected value: E(X) = Σ x·P(x), multiply each outcome by its probability and add. Binomial: with n independent trials and success probability p, P(X = k) = C(n, k)·pk·(1 - p)n-k, and the mean is np.
Try a similar one
The table shows the probability distribution of X. Find the expected value E(X).
| x | 1 | 6 | 8 |
|---|---|---|---|
| P(x) | 0.3 | 0.1 | 0.6 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Statistics & Probability
To count ways to choose r items from n, use C(n, r) = n! ÷ (r! × (n - r)!). For independent events, P(A and B) = P(A) × P(B); write the probability as a fraction in simplest form.
Try a similar one
How many ways can you choose 1 item from a set of 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distribution & z-Scores
The z-score z = (x - μ) / σ counts standard deviations from the mean. The 68-95-99.7 rule: about 68% of data lies within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ, so each band holds 34%, 13.5%, 2.35%, and 0.15% on each side.
Try a similar one
The exam scores are normally distributed with mean 63 and standard deviation 6. Find the z-score of a score of 57.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 12 Quiz: Data, Statistics & Probability — Easy Version 1
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.