6. A retail bakery makes cherry muffins where, due to the production process, \(15 \%\) of muffins contain a lower than expected quantity of cherries. The bakery sells these muffins in boxes of 20.

1. State a suitable distribution to model the number of muffins with a lower than expected quantity of cherries in a box, giving the value(s) of any parameter(s). State any assumptions needed for your model to be valid.
2. Using your model from part (a), find the probability that a randomly selected box contains:
   1. exactly 3 muffins with a lower than expected quantity of cherries,
   2. at least 5 muffins with a lower than expected quantity of cherries.
3. The bakery sells 25 boxes of muffins in one day. Find the probability that fewer than 4 of these boxes contain exactly 3 muffins with a lower than expected quantity of cherries.
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