2021 May TZ1 P2 Q3

A company produces bags of sugar whose masses, in grams, can be modelled by a normal distribution with mean \(1000\) and standard deviation \(3.5\). A bag of sugar is rejected for sale if its mass is less than \(995\) grams

1. Find the probability that a bag selected at random is rejected.

   [2]

2. Estimate the number of bags which will be rejected from a random sample of \(100\) bags.

   [1]

3. Given that a bag is not rejected, find the probability that it has a mass greater than \(1005\) grams.

   [3]