An examination consists of two parts: a written paper and a lab-based practical. Marks obtained by a

Question

An examination consists of two parts: a written paper and a lab-based practical. Marks obtained by a randomly chosen candidate follow normal distribution with means and standard deviations as shown in the following table. MeanStandard deviation Written paper$62$$\sigma$ Lab-based practical$56$$12$ It is given that the $95$th percentile score for the written paper is $85$ marks. Show that the value of $\sigma$ is $13.983$, correct to $5$ significant figures.[1] Find the probability that the difference between the marks obtained in the written paper and in the lab-based practical of a randomly chosen candidate is at least $9$.[3] The overall mark obtained for the examination is the total of $60$% of the mark obtained from written paper and $40$% of the mark obtained from lab-based practical. Find the probability that the overall mark of a randomly chosen candidate is less than $60$.[3] Find the smallest value of $n$ such that the probability that the mean overall mark of $n$ randomly chosen candidates being at least $58$ is at least $0.95$.[3] State an assumption needed for the calculations in part (b) to (d) to be valid and explain why the assumption may not be valid in practice.[2]

Accepted Answer

(b)0.643 (c)0.517 (d)99

2205 TJC P2 Q8

2205 TJC P2 Q8