Sophie was sick of her daily commute. ‘Why,’ she thought, ‘should I have to spend so much time in the morning stuck in traffic listening to some babbling half-wit on the radio? We can work flexi-time after all. Perhaps I should leave the apartment at some other time. So resolved, Sophie deliberately varied her time of departure from her usual 8.30. Also, being an organized soul, she recorded her time of departure each day and her journey time. Her records are shown in Table 18.4.

(a) Draw a scatter diagram that will help Sophie decide on the best time to leave her apartment.
(b) How much time per (five-day) week should she expect to be saved from having to listen to a babbling half-wit?

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Table 18.4 Sophie's journey times (in minutes) Day Leaving time Day 1 2 3 4 5 7.15 8.15 7.30 7.20 8.40 Journey time 19 40 25 19 46 6 7 ܘ ܘ ܣ ܂ 8 9 10 Leaving time 8.45 8.55 7.55 7.40 8.30 Journey time 40 32 31 22 49 Day 11 12 13 14 15 Leaving time 8.35 8.40 8.20 8.00 7.45 Journey time 46 45 47 34 27