9 At the beginning of the academic year, all the pupils in year 12 at a college take part in an assessment. Summary statistics for the marks obtained by the 2021 cohort are given below.
\(n = 205 \sum x = 23042 \sum x ^ { 2 } = 2591716\)
Marks may only be whole numbers, but the Head of Mathematics believes that the distribution of marks may be modelled by a Normal distribution.
- Calculate
- The mean mark
- The variance of the marks
- Use your answers to part (a) to write down a possible Normal model for the distribution of marks.
One candidate in the cohort scored less than 105. - Determine whether the model found in part (b) is consistent with this information.
- Use the model to calculate an estimate of the number of candidates who scored 115 marks.