A-LevelMathematicsProbability and statistics9709/63 · May/June 2018 · Q47 Marks

Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recorded in the table below, together with the means and standard deviations of the prices. Number of Mean price Standard holidays () deviation () Farfield Travel 30 1500 230 Lacket Travel 21 2400 160

(i)Calculate the mean price of all 51 holidays.[2]
(ii)The prices of individual holidays with Farfield Travel are denoted by x_(F) and the prices of individual holidays with Lacket Travel are denoted by x_(L). By first finding Σx_F² and Σx_L², find the standard deviation of the prices of all 51 holidays.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[2] M1 Multiply by 30 and 21, summing and dividing total by 51 (45000+50400)/51
[2] A1 correct answer (to 3sf)
[5] M1 One correct substitution into a correct variance formula
[5] A1 Correct Σx_F² (rounding to 69 000 000 2sf)
[5] A1 Correct Σx_L² (rounding to 121 000 000 3sf)
[5] M1 using 'Σx_F²'+ '' Σx_L² dividing by 51 and subtracting ‘i' squared. (Correct ‘Σx_F² + ‘' Σx_L² = 190 584 600)
[5] A1 Correct answer accept anything between 486 and 490

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