19N.1.SL.TZ0.T_13

pestleMathematicsAISLPaper 119N· sl-4-2-histograms-cf-graphs-box-plotssource ↗

Chicken eggs are classified by grade ( $4$ , $5$ , $6$ , $7$ or $8$ ), based on weight. A mixed carton contains $12$ eggs and could include eggs from any grade. As part of the science project, Rocky buys $9$ mixed cartons and sorts the eggs according to their weight.

State whether the weight of the eggs is a continuous or discrete variable.

[1]

Write down the modal grade of the eggs.

[1]

Use your graphic display calculator to find an estimate for the standard deviation of the weight of the eggs.

[2]

The mean weight of these eggs is 64.9 grams, correct to three significant figures.

Use the table and your answer to part (c) to find the smallest possible number of eggs that could be within one standard deviation of the mean.

[2]

Markscheme / solution

continuous (A1) (C1)

[1 mark]

$6$ (A1) (C1)

Note: Award (A0) for an answer of $60 \leq w < 70$ .

[1 mark]

$8.97 (8.97479 \dots)$ (g) (A2) (C2)

[2 marks]

$[55.9, 73.9]$ OR $55.9252 \dots \leq w \leq 73.8747 \dots$ (M1)

Note: Award (M1) for correct endpoints seen. If the answer to part (c) is $14.1421 \dots$ , award (M1) for endpoints of $[50.7578 \dots, 79.0421 \dots]$ .

$45$ (A1)(ft) (C2)

Note: Follow through from their part (c). For a standard deviation between $0$ and $5$ inclusive, the FT answer is $0$ .

[2 marks]

Examiners’ report

[N/A]