The weights of bananas in a fruit shop have a normal distribution with mean 150 grams and standard deviation 50 grams. Three sizes of banana are sold.

Small: under 95 grams
Medium: between 95 grams and 205 grams
Large: over 205 grams

1. Find the proportion of bananas that are small.
2. Find the weight exceeded by 10% of bananas.

The prices of bananas are 10 cents for a small banana, 20 cents for a medium banana and 25 cents for a large banana.

3. (a) Show that the probability that a randomly chosen banana costs 20 cents is 0.7286.
4. (b) Calculate the expected total cost of 100 randomly chosen bananas.