3 Each day, Margot completes the crossword in her local morning newspaper. Her completion times, \(X\) minutes, can be modelled by a normal random variable with a mean of 65 and a standard deviation of 20 .
- Determine:
- \(\mathrm { P } ( X < 90 )\);
- \(\mathrm { P } ( X > 60 )\).
- Given that Margot's completion times are independent from day to day, determine the probability that, during a particular period of 6 days:
- she completes one of the six crosswords in exactly 60 minutes;
- she completes each crossword in less than 60 minutes;
- her mean completion time is less than 60 minutes.
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