The value of X that is exceeded for 10% of the measurement duration is:
2011
The value of X that is exceeded for 10% of the measurement duration is:
Answer: B. 68 — ConceptFor N equally spaced measurements, a value exceeded for p% of the duration has (p/100) × N measurements strictly greater than it. Sort the observations…
- A.
69
- B.
68
- C.
67
- D.
66
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Correct answer: B
Concept
For N equally spaced measurements, a value exceeded for p% of the duration has (p/100) × N measurements strictly greater than it.
Sort the observations in descending order and identify the threshold immediately after that number of exceedances.
Application
There are 20 measurements, so 10% of 20 is 2.
In descending order, the largest readings begin 70, 69, 68, 67, 66.
Exactly two readings, 70 and 69, are strictly greater than 68.
Cross-check
The proportion of readings above 68 is 2/20 = 10%. In contrast, only 1/20 = 5% lies above 69, while 3/20 = 15% lies above 67.
Therefore, the required value of X is 68.