The proportion of the available motorcycles that Molly can afford is 60%.
The 30th percentile for the motorcycle is $11920
It should be noted that $25,000 is considered an outlier because it is greater than $24792
Since, mean, μ = $14,000 and standard deviation, σ = $4,000, the standard variable Z or x = $15,000 will be:
Z = (x - μ)/σ
Z = (15000 - 14000)/4000
Z = 0.25
We then check the table and see that it implies that Molly can buy 60% of the available motorcycles.
The 30th percentile for the prices of motorcycles of this type corresponds to a value of Z = -0.52. This will then be:
x = μ + Z*σ
x = 14000 + (-0.52) × 4000
x = $11920
Lastly, the third quartile value when added to 1.5 x IQR will be equal to:
= 16698 + (1.5 × 5396) = $24792
Therefore, $25,000 is considered an outlier because it is greater than $24792
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