Normal tail probabilities for loaf masses shown on a sketch, the probability between two masses and binomial counts in a pack

A bakery makes loaves of bread whose masses are normally distributed with mean \(800\) grams and standard deviation \(25\) grams.

1. One loaf is chosen at random.
   1. Find the probability that the mass of the loaf is less than \(760\) grams.
   2. Find the probability that the mass of the loaf is more than \(830\) grams.
   3. The diagram below shows the normal curve for the masses of the loaves. On the diagram, shade the regions whose areas are the probabilities found in (i) and (ii), and label each region.
   4. Hence show that the probability that the mass of the loaf is between \(760\) grams and \(830\) grams is \(0.8301\), correct to four significant figures.[7]
2. A café buys a pack of \(12\) of these loaves. The masses of the loaves are independent.
   1. Find the probability that every loaf in the pack has a mass between \(760\) grams and \(830\) grams.
   2. Find the probability that at least \(10\) of the loaves in the pack have a mass between \(760\) grams and \(830\) grams.[6]