3 The weights of Braeburn apples on display in a supermarket, measured in grams, are Normally distributed with mean 210.5 and standard deviation 15.2.

1. Find the probability that a randomly selected apple weighs at least 220 grams.
2. These apples are sold in packs of 3. You may assume that the weights of apples in each pack are independent. Find the probability that all 3 of the apples in a randomly selected pack weigh at least 220 grams.
3. 100 packs are selected at random.
   (A) State the exact distribution of the number of these 100 packs in which all 3 apples weigh at least 220 grams.
   (B) Use a suitable approximating distribution to find the probability that in at most one of these packs all 3 apples weigh at least 220 grams.
   (C) Explain why this approximating distribution is suitable.
4. The supermarket also sells Cox's Orange Pippin apples. The weights of these apples, measured in grams, are Normally distributed with mean 185 and standard deviation \(\sigma\).
   (A) Given that \(10 \%\) of randomly selected Cox's Orange Pippin apples weigh less than 170 grams, calculate the value of \(\sigma\).
   (B) Sketch the distributions of the weights of both types of apple on a single diagram.