SPS SPS SM Statistics 2024 January — Question 1

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2024
SessionJanuary
TopicNormal Distribution
TypeEstimate from summary statistics

1. 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.
\(n = 205 \quad \sum x = 23042 \quad \sum x ^ { 2 } = 2591716\) Marks may only be whole numbers, but the Head of Mathematics believes that the distribution of marks may be modelled by a Normal distribution.
  1. 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.