misswelton.weebly.com · web viewquestion 3: the normal distributioncandidates showed comprehensive...

4.1

1a. [2 marks]

Markscheme

(M1)

Note: Award (M1) for diagram that shows the correct shaded area and percentage, k has to be greater

than the mean.

OR

Award (M1) for P(mark > k) = 0.1 or P(mark ≤ k) = 0.9 seen.

428 (428.155…) (A1) (C2)

[2 marks]

Examiners report

[N/A]

1b. [2 marks]

Markscheme

1

(M1)

Note: Award (M1) for diagram that shows the correct shaded area and the value 450 labelled to the

right of the mean.

OR

Award (M1) for P(mark ≥ 450) seen.

0.0668 (0.0668072…, 6.68 %, 6.68072… %) (A1) (C2)

[2 marks]

Examiners report

[N/A]

1c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for 0.0228 (0.0227500…) seen. Accept 1 − 0.97725.

= 0.341 (0.340532…, 34.1 %, 34.0532…%) (A1)(ft) (C2)

Note: Follow through from part (b), provided answer is between zero and 1.

2

[2 marks]

Examiners report

[N/A]

2a. [2 marks]

Markscheme

0.0548 (0.054799…, 5.48%) (A2) (C2)

[2 marks]

Examiners report

[N/A]

2b. [2 marks]

Markscheme

0.645 (0.6449900…, 64.5%) (A2) (C2)

3

[2 marks]

Examiners report

[N/A]

2c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for dividing 15 by their part (a)(i).

Accept an equation of the form 15 = x × 0.0548 for (M1).

274 (273.722…) (A1)(ft) (C2)

Note: Follow through from part (a)(i). Accept 273.

[2 marks]

Examiners report

[N/A]

3a. [2 marks]

Markscheme

P(W < 61) (M1)

4

Note: Award (M1) for correct probability statement.

OR

(M1)

Note: Award (M1) for correct region labelled and shaded on diagram.

= 0.212 (0.21185…, 21.2%) (A1)(G2)

[2 marks]

Examiners report

[N/A]

3b. [2 marks]

Markscheme

40 × 0.21185… (M1)

Note: Award (M1) for product of 40 and their 0.212.

= 8.47 (8.47421...) (A1)(ft)(G2)

Note: Follow through from their part (a)(i) provided their answer to part (a)(i) is less than 1.

[2 marks]

Examiners report

[N/A]

3c. [2 marks]

Markscheme

5

(A1)(M1)

Note: Award (A1) for two correctly labelled vertical lines in approximately correct positions. The

values 57.5 and 72.5, or μ − 1.5σ and μ + 1.5σ are acceptable labels. Award (M1) for correctly shaded

region marked by their two vertical lines.

[2 marks]

Examiners report

[N/A]

3d. [1 mark]

Markscheme

0.866 (0.86638…, 86.6%) (A1)(ft)

Note: Follow through from their part (b)(i) shaded region if their values are clear.

[1 mark]

Examiners report

[N/A]

3e. [2 marks]

Markscheme

P(W < k) = 0.775 (M1)

OR

6

(M1)

Note: Award (A1) for correct region labelled and shaded on diagram.

(k =) 68.8 (68.7770…) (A1)(G2)

[2 marks]

Examiners report

[N/A]

3f. [1 mark]

Markscheme

(H0:) performance (of players) and (their) weight are independent. (A1)

Note: Accept “there is no association between performance (of players) and (their) weight”. Do not

accept "not related" or "not correlated" or "not influenced".

[1 mark]

Examiners report

[N/A]

3g. [2 marks]

Markscheme

0.287 (0.287436…) (G2)

[2 marks]

Examiners report

[N/A]

7

3h. [2 marks]

Markscheme

accept/ do not reject null hypothesis/H0 (A1)(ft)

OR

performance (of players) and (their) weight are independent. (A1)(ft)

0.287 > 0.05 (R1)(ft)

Note: Accept p-value>significance level provided their p-value is seen in b(ii). Accept 28.7% > 5%. Do

not award (A1)(R0). Follow through from part (d).

[2 marks]

Examiners report

[N/A]

4a. [2 marks]

Markscheme

0.787 (0.787433…, 78.7%) (M1)(A1) (C2)

Note: Award (M1) for a correct probability statement, , or a correctly shaded normal

distribution graph.

[2 marks]

Examiners report

8

[N/A]

4b. [2 marks]

Markscheme

73.0 (minutes) (72.9924…) (M1)(A1) (C2)

Note: Award (M1) for a correct probability statement, , or a correctly shaded

normal distribution graph.

[2 marks]

Examiners report

[N/A]

4c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for multiplying a probability by 400. Do not award (M1) for .

Use of a lower bound less than zero gives a probability of 0.0429172….

(A1) (C2)

9

Notes: Accept a final answer of 17. Do not accept a final answer of 18. Accept a non-integer final

answer either 16.9 (16.9373…) from use of lower bound zero or 17.2 (17.1669…) from use of the

default lower bound of .

[2 marks]

Examiners report

[N/A]

5a. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

[N/A]

5b. [2 marks]

Markscheme

OR (M1)

Note: Award (M1) for a sketch of approximate normal curve with a vertical line drawn to the right of

the mean with the area to the right of this line shaded.

(A1) (C2)

[2 marks]

Examiners report

[N/A]

10

5c. [3 marks]

Markscheme

(A1)(ft)(M1)

Note: Award (A1)(ft) for seen, award (M1) for multiplying

their 33.7244… by 2. Follow through from their answer to part (b).

OR

(A1)(ft)(M1)

Note: Award (A1)(ft) for their seen, (M1) for difference between their answer to

(b) and their 366.

OR

(A1)(ft)(M1)

Note: Award (A1)(ft) for their seen. Award (M1) for correct symmetrical region

indicated on labelled normal curve.

67.4 (g) (A1)(ft) (C3)

11

Note: Accept an answer of 68 from use of rounded values. Follow through from part (b).

[3 marks]

Examiners report

[N/A]

6a. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution into mean formula.

(A1) (G2)

[2 marks]

Examiners report

[N/A]

6b. [1 mark]

Markscheme

(G1)

[1 mark]

Examiners report

[N/A]

6c. [1 mark]

Markscheme

12

5 (A1)

[1 mark]

Examiners report

[N/A]

6d. [2 marks]

Markscheme

(M1)

Note: Award (M1) for 6 and 4 seen.

(A1) (G2)

[2 marks]

Examiners report

[N/A]

6e. [2 marks]

Markscheme

(M1)

Note: Award (M1) for seen.

(A1) (G2)

[2 marks]

Examiners report

13

[N/A]

6f. [3 marks]

Markscheme

(M1)(M1)

Note: Award (M1) for seen, (M1) for multiplying their first probability by .

OR

Note: Award (M1) for seen, (M1) for dividing their first probability by .

(A1)(ft) (G3)

Note: Follow through from part (d).

[3 marks]

Examiners report

[N/A]

6g. [2 marks]

Markscheme

(M1)

14

OR

(M1)

Note: Award (M1) for a diagram showing the correct shaded region .

(A1) (G2)

[2 marks]

Examiners report

[N/A]

6h. [2 marks]

Markscheme

(M1)

(A1)(ft) (G2)

Note: Follow through from part (f)(i).

[2 marks]

Examiners report

[N/A]

15

7a. [2 marks]

Markscheme

(A1)(A1)

Notes: Award (A1) for bell shape with mean of 502.

Award (A1) for an indication of standard deviation eg 500 and 504.

[2 marks]

Examiners report

[N/A]

7b. [4 marks]

Markscheme

(i) (G2)

Note: Award (M1) for a diagram showing the correct shaded region.

(ii) (M1)

16

(A1)(ft)(G2)

Note: Follow through from their answer to part (b)(i).

[4 marks]

Examiners report

[N/A]

7c. [2 marks]

Markscheme

(M1)

Notes: Award (A1) for .

OR

(M1)

Notes: Award (M1) for .

(A1)(ft)(G2)

[2 marks]

Examiners report

[N/A]

7d. [3 marks]

17

Markscheme

(G3)

Notes: Award (G2) for an answer that rounds to 346.

Award (G1) for seen without working (for finding the top 3%).

[3 marks]

Examiners report

[N/A]

8a. [1 mark]

Markscheme

(A1) (C1)

Examiners report

Question 8: Normal distribution

Part (a) was correctly answered by the majority.

8b. [2 marks]

Markscheme

(A2)(ft) (C2)

18

Examiners report

Part (b) was generally well attempted by those who had studied this part of the course. However, it was

clear that many centres simply do not teach this part of the course.

8c. [3 marks]

Markscheme

(A2)(ft)

(A1)(ft) (C3)

Examiners report

In part (c), the two common faults were calculation of the bottom “tail” and incorrect rounding.

19

9a. [2 marks]

Markscheme

(A1)(A1)

Note: Award (A1) for normal curve with mean of indicated or two vertical lines drawn

approximately in correct place. Award (A1) for correct shaded region (between the vertical lines.).

Examiners report

Question 3: The normal distribution

Candidates showed comprehensive understanding of the normal distribution. The graphic display

calculator was used efficiently by most of the candidates. There was much variability in the ability to

sketch the curve in part (a). Instead of drawing the straight-forward sketch with the mean line and two

vertical lines as required at 60 and 70, many linked it to standard deviations. It was very rare to see any

method in part (c). Most candidates managed part (d)(i) but few went on to complete part (d)(ii).

9b. [3 marks]

Markscheme

(i) (G1)

(ii) (G1)

(iii) (G1)

Examiners report



20





9c. [2 marks]

Markscheme

OR (M1)

OR

(M1)

Note: Award (M1) for the correct probability equation OR for a correct region indicated on labelled

diagram.

(A1)(G2)

Note: Award (M1) for any correct method.

Examiners report







9d. [4 marks]

Markscheme

21

(i) (M1)

Note: Award (M1) for dividing by .

(A1)(G2)

(ii) (or equivalent) (M1)

(vehicles) (A1)(ft)(G2)

Note: Award (M1) for correct method. Follow through from their part (d)(i).

Examiners report







10a. [2 marks]

Markscheme

(M1)

22

Note: Award (M1) for approximate curve with 990 and 1004 in correct place.

(A1) (C2)

Examiners report

A significant number of candidates did not answer this question. It was very rare that a correct method

was shown for any of the parts of this question. Often a normal distribution graph was drawn with

indication of the mean and multiples of the standard deviation, with indication of the corresponding

probabilities, but not a diagram identifying the area under the curve corresponding to the questions.

There were however many correct answers for part (a). For part (b) many answered incorrectly; the

most common incorrect answer was 1008, resulting from adding 2 sd to the mean. Very few correct

answers were given for part (c).

10b. [2 marks]

Markscheme

(M1)

Note: Award (M1) for approximate curve with placed to the right of the mean.

(A1) (C2)

Note: Award full marks only for , or an answer with more than sf resulting from correct

rounding of .

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Examiners report








10c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for some indication of symmetry on diagram.

OR

OR (M1)

Note: Award (M1) for probability with single inequality resulting from symmetry of diagram.

(A1) (C2)

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Examiners report








11a. [2 marks]

Markscheme

(A1)(M1) (C2)

Notes: Award (A1) for the vertical line labelled as .

Award (M1) for a vertical line drawn to the left of the mean with the area to the left of this line shaded.

Accept sd marked on the diagram for (provided line is to the left of the mean).

Examiners report

[N/A]

11b. [4 marks]

Markscheme

(i) (A1)(C1)

(ii) (A1)(M1)

Note: Award (A1) for the vertical line labelled as .

25

Award (M1) for a vertical line drawn to the right of the mean with the area to the right of this line

shaded.

Accept 1 sd marked on the diagram for (provided line is to the right of the mean).

(A1) (C3)

Examiners report

[N/A]

12a. [3 marks]

Markscheme

(i) (G2)

Notes: Award (M1) for an attempt to use the formula for the mean with a least two rows from the table.

(ii) (G1)

Examiners report

[N/A]

12b. [3 marks]

Markscheme

(M1)(A1)

Notes: Award (M1) for attempting to use the normal distribution to find the probability or for correct

region indicated on labelled diagram. Award (A1) for correct probability.

(A1)(ft)(G3)

Notes: Award (A1)(ft) for converting their probability into a percentage.

Examiners report

26

[N/A]

12c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for attempting to use the normal distribution to find the probability or for correct

region indicated on labelled diagram.

(A1)(G2)

Examiners report

[N/A]

12d. [2 marks]

Markscheme

(M1)

Note: Award (M1) for subtracting “ their part (b)” from 100 or (M1) for attempting to use the

normal distribution to find the probability or for correct

region indicated on labelled diagram.

(A1)(ft)(G2)

Notes: Follow through from their answer to part (b). Percentage symbol is not required. Accept

( ) if used.

Examiners report

[N/A]

12e. [2 marks]

Markscheme

27

(M1)

Note: Award (M1) for multiplying by (or ).

(A1)(G2)

Examiners report

[N/A]

13a. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correctly shaded area.

(A1) (C2)

Examiners report

[N/A]

13b. [2 marks]

Markscheme

(M1)

Note: Award (M1) for multiplying by .

28

(A1)(ft) (C2)

Note: Follow through from part (a).

Examiners report

[N/A]

13c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correctly shaded area.

(A1) (C2)

Examiners report

[N/A]

14a. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

[N/A]

29

14b. [1 mark]

Markscheme

(A1) (C1)

Note: Accept or .

[1 mark]

Examiners report

[N/A]

14c. [2 marks]

Markscheme

(M1)

Note: Accept alternative methods.

(A1) (C2)

[2 marks]

Examiners report

[N/A]

14d. [2 marks]

30

Markscheme

(M1)

Note: Accept alternative methods.

(A1) (C2)

[2 marks]

Examiners report

[N/A]

15a. [2 marks]

Markscheme

(A1)(A1)

Notes: Award (A1) for rough sketch of normal curve centred at , (A1) for some indication of as

the standard deviation eg, as diagram, or with and shown on the horizontal axis in appropriate

places, or for and shown on the horizontal axis in appropriate places.

31

[2 marks]

Examiners report

[N/A]

15b. [1 mark]

Markscheme

(A1)

Note: Accept only the exact answer.

[1 mark]

Examiners report

[N/A]

15c. [2 marks]

Markscheme

(G2)

Note: Award (G1) for , award (M1)(G0) for diagram with correct area shown but

incorrect answer.

[2 marks]

Examiners report

[N/A]

15d. [2 marks]

Markscheme32

(G2)

Note: Award (G1) for , award (M1)(G0) for diagram with correct area shown but

incorrect answer.

[2 marks]

Examiners report

[N/A]

15e. [2 marks]

Markscheme

(R1)

Notes: Award (R1) for correct comparison seen. Accept alternative methods, for example, (their

answer to part (c)) used in comparison or a comparison based on scores.

the Physics result is better (A1)(ft)

Notes: Do not award (R0)(A1). Follow through from their answers to part (c) and part (d).

[2 marks]

Examiners report

[N/A]

15f. [3 marks]

Markscheme

33

(G3)

Notes: Award (G1) for , award (G2) for .

Award (M1)(G0) for diagram with correct area shown but incorrect answer.

[3 marks]

Examiners report

[N/A]

16a. [3 marks]

Markscheme

(A1) for normal curve with mean of indicated

(A1) for three lines in approximately the correct position

(A1) for labels on the three lines (A1)(A1)(A1)

Examiners report

[N/A]

16b. [4 marks]

Markscheme

34

(i) ( ) (M1)(A1)(G2)

Note: Award (M1) for correct region indicated on labelled diagram.

(ii) ( ) (M1)(A1)(G2)


Examiners report

[N/A]

16c. [2 marks]

Markscheme

(M1)

( ) (A1)(G2)


Examiners report

[N/A]

16d. [2 marks]

Markscheme

Expected number of large size eggs

(M1)

(A1)(G2)

Examiners report

[N/A]

16e. [3 marks]

35

Markscheme

Expected income

(M1)(M1)

Note: Award (M1) for their correct products, (M1) for addition of 4 terms.

(A1)(ft)(G3)

Note: Follow through from part (b).

Examiners report

[N/A]

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