A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal distribution with a mean diameter of 5.85 cm and a standard deviation of 0.24 cm. For each of the following, sketch the graph and solve.
- Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm.
- The middle 20% of mandarin oranges from this farm have diameters between ___ and ____.
- Find the 90th percentile for the diameters of mandarin oranges, and interpret it in a complete sentence.