5 Hebe attempts a crossword puzzle every day. The number of puzzles she completes in a week (7 days) is denoted by \(X\).
- State two conditions that are required for \(X\) to have a binomial distribution.
On average, Hebe completes 7 out of 10 of these puzzles. - Use a binomial distribution to find the probability that Hebe completes at least 5 puzzles in a week.
- Use a binomial distribution to find the probability that, over the next 10 weeks, Hebe completes 4 or fewer puzzles in exactly 3 of the 10 weeks.