6 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
- Find the proportion of bananas that are small.
- 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.
- (a) Show that the probability that a randomly chosen banana costs 20 cents is 0.7286 .
(b) Calculate the expected total cost of 100 randomly chosen bananas.