21M.1.AHL.TZ1.14

pestleMathematicsAIHLPaper 121M· sl-4-9-normal-distribution-and-calculationssource ↗

The weights of apples from Tony’s farm follow a normal distribution with mean $158 g$ and standard deviation $13 g$ . The apples are sold in bags that contain six apples.

Find the mean weight of a bag of apples.

[2]

Find the standard deviation of the weights of these bags of apples.

[2]

Find the probability that a bag selected at random weighs more than $1 kg$ .

[2]

Markscheme / solution

$158 \times 6 = 948 (g)$ (M1)A1

[2 marks]

variance $6 \times 13^{2}$ (M1)

$SD = 31.8 (g) (13 \sqrt{6}, 31.8433 \dots)$ A1

[2 marks]

$X ~ N (948, 31.8433 \dots^{2})$

$P (X > 1000) = 0.0512 (0.0512350 \dots)$ (M1)A1

Note: Accept $0.0510 (0.0510014 \dots)$ if $3$ sf value $31.8$ is used.
Award (M1)A1FT if the answer is correct for their SD, even if no working is shown. e.g. If the SD is $78$ then accept $0.252$ .

[2 marks]

Examiners’ report

[N/A]