In Australia, we are blessed with many wildly different coffee bean options. A crowd-pleaser is Sensory Lab, whose rating is assumed to follow a normal distribution with a mean of = 72.2 on a 100 point scale and a standard deviation of = 6.1.

What probability does a randomly selected batch from Sensory Lab have a rating greater than 84.7? (3dp)

What probability does a randomly selected batch from Sensory Lab have a rating lower than 63.2? (3dp)

What probability does a randomly selected batch from Sensory Lab have a rating between 64.1 and 85.9? (3dp)

What is the rating of a randomly selected batch with a z-score of -0.6? (3dp)

For a coffee batch randomly selected from Sensory Lab to qualify as one of the premium batches, it must have a rating greater than 85.9. If there are 40 coffee bean batches, how many do you think will be considered premium? (integer)