A crossword puzzle is published in The Times. each day of the week, except Sunday. A woman is able to complete, on average, eight out of ten the crossword puzzles. of

(a) Find the expected value and the standard deviation of the number of completed crosswords in a given week.

(b) Show that the probability that she will complete at least five in a given week is 0.655 (to three significant figures).

(c) Given that she completes the puzzle on Monday, find, to three significant figures, the probability that she will complete at least four in the rest of the week.

(d) Find, to three significant figures, the probability that, in a period of four weeks, she completes four or less in only one of the four weeks. (C)