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In Australia, we are blessed with many wildly different coffee bean options. A crowd-pleaser is Single O, whose rating is assumed to follow a normal distribution with a mean of = 79.6 on a 100 point scale and a standard deviation of = 9.1.

Draw diagrams to help you solve the following problems

(1 mark) What probability does a randomly selected batch from Single O have a rating greater than 86.1? Answer (3dp)

(1 mark) What probability does a randomly selected batch from Single O have a rating lower than 61? Answer (3dp)

(2 mark) What probability does a randomly selected batch from Single O have a rating between 69 and 82? Answer (3dp)

(1 mark) What is the rating of a randomly selected batch with a z-score of -0.3? Answer (3dp)

(1 mark) For a coffee batch randomly selected from Single O to qualify as one of the premium batches, it must have a rating greater than 82. If there are 30 coffee bean batches, how many do you think will be considered premium? Answer (integer)