Calculate normal interval probabilities, shade a curve and apply a binomial model to a batch.

The weights of chickens for sale in a shop are normally distributed with mean 2.5 kg and standard deviation 0.3 kg.

1. A chicken is chosen at random.[7]
   1. Find the probability that it weighs less than 2 kg.
   2. Find the probability that it weighs more than 2.8 kg.
   3. Copy the diagram below. Shade the areas that represent the probabilities from parts (i) and (ii).
   4. Hence show that the probability that it weighs between 2 kg and 2.8 kg is 0.7936 (to four significant figures).
2. A customer buys 10 chickens.[6]
   1. Find the probability that all 10 chickens weigh between 2 kg and 2.8 kg.
   2. Find the probability that at least 7 of the chickens weigh between 2 kg and 2.8 kg.