Unknown normal mean and standard deviation from two tail percentages, then binomial and conditional probabilities

The masses, \(M\) grams, of apples from an orchard are normally distributed with standard deviation \(\sigma\) and mean \(\mu\). The masses of different apples are independent.

Of these apples, \(4.5\%\) have a mass below \(150\) grams and \(9.2\%\) have a mass above \(210\) grams.

1. 1. Find \(\mu\) and \(\sigma\).
   2. Hence find, for a randomly chosen apple, the probability that its mass is between \(160\) grams and \(200\) grams.[7]

Apples are packed into bags of \(15\). Each apple, independently of the others, is free of blemishes with probability \(0.885\).

2. 1. Find the probability that a randomly chosen bag contains at least \(12\) blemish-free apples.
   2. A bag is known to contain at least \(12\) apples that are free of blemishes. Find the probability that it contains more than one blemished apple.[7]