12 Using the information from Example 6.12, answer the following: a. The middle 40% of mandarin oranges from this farm are between and b. Find the 16th percentile and interpret it in a complete sentence.
Example 6.12
A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a
a. Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm. Sketch the graph.
b. The middle 20% of mandarin oranges from this farm have diameters between ______ and ______.
c. Find the 90th percentile for the diameters of mandarin oranges, and interpret it in a complete sentence.
Solution 1
a. normalcdf(6,10^99,5.85,0.24) = 0.2660
b.
- 1 - 0.20 = 0.80
- The tails of the graph of the normal distribution each have an area of 0.40.
- Find k1, the 40th percentile, and k2, the 60th percentile (0.40 + 0.20 = 0.60).
- k1 = invNorm(0.40,5.85,0.24) = 5.79 cm
- k2 = invNorm(0.60,5.85,0.24) = 5.91 cm
c. 6.16: Ninety percent of the diameter of the mandarin oranges is at most 6.16 cm.
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