• Quick retrieval from earlier learning (Combine regions of a normal curve with the 68–95–99.7 rule; Calculate and use z-scores). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A test has mean 70 and standard deviation 5. Find the z-score of a mark of 77.5. → 1.5Prompt: z = (x − mean) ÷ standard deviation.
2. A quantity is normally distributed with mean 42 and standard deviation 2. What percentage of values lie between 36 and 44? → 83.85Prompt: Convert each end to 'number of standard deviations from the mean'.
3. A factory fills 400 bottles. Volumes are normally distributed with mean 454 ml and standard deviation 20 ml. About how many bottles hold more than 494 ml? → 10Prompt: That value is 2 standard deviations from the mean.

• Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
• Share the objective: Find normal probabilities with z-scores and technology. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: X is normally distributed with mean 153 and standard deviation 20. Find P(X < 134.8) to 3 decimal places.
• Step 1: z = (134.8 − 153)/20 ≈ −0.91
• Step 2: P ≈ 0.181
• Answer: 0.181
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. X is normally distributed with mean 173 and standard deviation 11. Find P(X < 152.5) to 3 decimal places. → 0.031Prompt: Standardise: z = (x − μ)/σ.
2. Battery life is normally distributed with mean 271 minutes and standard deviation 13 minutes. Find the probability that a battery lasts between 261 and 293 minutes, to 3 decimal places. → 0.734Prompt: P(a < X < b) = P(X < b) − P(X < a).

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. Adult heights are normally distributed with mean 184 cm and standard deviation 6 cm. Find P(height > 186 cm) to 3 decimal places. → 0.369Prompt: P(X > x) = 1 − P(X < x).
2. X is normally distributed with mean 151 and standard deviation 19. Find P(X < 167.7) to 3 decimal places. → 0.81Prompt: Standardise: z = (x − μ)/σ.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.