1. **Problem statement:** We have a class of 40 students with 25 taking Biology, 18 taking Chemistry, and 8 taking both subjects. (i) Draw a Venn diagram to represent this information. (ii) Find the probability that a student is registered for neither Chemistry nor Biology. b) Heights of dwarf cocoa plants are normally distributed with mean $\mu=120$ cm and standard deviation $\sigma=8$ cm. (i) Find the probability that a randomly selected plant is taller than 130 cm. --- ### Part a(i): Venn Diagram - Total students: 40 - Biology only: $25 - 8 = 17$ - Chemistry only: $18 - 8 = 10$ - Both Biology and Chemistry: 8 - Neither: $40 - (17 + 10 + 8) = 5$ ### Part a(ii): Probability of neither subject $$P(\text{neither}) = \frac{5}{40} = 0.125$$ ### Part b(i): Probability plant taller than 130 cm 1. Standardize the height using the Z-score formula: $$Z = \frac{X - \mu}{\sigma} = \frac{130 - 120}{8} = 1.25$$ 2. Find $P(Z > 1.25)$ using standard normal distribution tables or calculator: $$P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056$$ **Final answers:** - Probability student registered for neither subject: $0.125$ - Probability plant taller than 130 cm: $0.1056$