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In an ordered list of 20 delivery times, 12 times are shorter than Ravi's time and 2 times, including his, equal it. Using the expression (x + 0.5y)(100)/n, at what percentile is Ravi's time?
AThe 60th percentile
BThe 70th percentile
CThe 55th percentile
DThe 65th percentile
Answer & Solution
Correct answer: D. The 65th percentile
1. In the percentile expression, x counts values below the target and y counts values equal to it.
2. Here x = 12 shorter times, y = 2 equal times, and n = 20 values in all.
3. Substitute: (12 + 0.5 x 2)(100)/20 = (13)(100)/20.
4. That equals 1300/20 = 65, so Ravi's time sits at the 65th percentile.
5. Option A, the 60th, forgets the 0.5y correction and uses only the 12 values below.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.2 Measures of the Location of the Data_
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