1. **Problem statement:** (a)(i) In a class of 40 students, 20 take Science, 10 take Chemistry, and 5 take both Science and Chemistry. Draw a Venn diagram to represent this. (a)(ii) Find the probability that a student is registered for neither Chemistry nor Biology. (b)(i) Heights of dwarf cocoa plants are normally distributed with mean $\mu=120$ cm and standard deviation $\sigma=8$ cm. Find the probability a randomly selected plant is taller than 120 cm. --- 2. **Solution for (a)(i): Venn diagram setup** - Total students: 40 - Science only: $20 - 5 = 15$ - Chemistry only: $10 - 5 = 5$ - Both Science and Chemistry: 5 - Neither Science nor Chemistry: $40 - (15 + 5 + 5) = 15$ The Venn diagram has two overlapping circles labeled Science and Chemistry with the numbers 15, 5, and 5 in the respective regions, and 15 outside both circles. --- 3. **Solution for (a)(ii): Probability of neither Chemistry nor Biology** Assuming Biology is not taken by any student (or no data given), the question reduces to neither Science nor Chemistry. Number of students taking Science or Chemistry = $15 + 5 + 5 = 25$ Number taking neither = 15 Probability = $\frac{15}{40} = 0.375$ --- 4. **Solution for (b)(i): Probability plant taller than 120 cm** Given $X \sim N(120, 8^2)$, find $P(X > 120)$. Calculate the z-score: $$z = \frac{120 - 120}{8} = 0$$ From standard normal distribution, $P(Z > 0) = 0.5$. Therefore, the probability a plant is taller than 120 cm is 0.5. --- **Final answers:** - (a)(ii) Probability neither Chemistry nor Biology = 0.375 - (b)(i) Probability plant taller than 120 cm = 0.5