100 randomly chosen adults each throw a ball once. The length, l metres, of each throw is recorded. The results are summarised below. n = 100 Σl = 3820 Σl² = 182 200

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [B1] Mean `l-bar = 3820/100 = 38.2`
2. [M1] For calculating unbiased variance: `(100/99) * (182200/100 - 38.2^2)` or `(1/99) * (182200 - 3820^2/100)`. Use of biased (362.76) scores M0.
3. [A1] Unbiased variance `s^2 = 12092/33` or `366.424` or `366 (3 sf)`. Accept SD=`19.1422` or `19.1(3sf)`.
4. [M1] For confidence interval formula: `'38.2' ± z * sqrt('366.424'/100)`. Expression of the correct form must be a z-value.
5. [B1] For `z = 1.881` or `1.882`.
6. [A1] Confidence interval `34.6` to `41.8 (3 sf)`. Allow use of biased giving `(34.6,41.8)`. Must be an interval.