This Exam P sample reference tests Exponential Distribution. The four-hour median fixes the exponential survival curve. Raising 0.5 to the 5/4 power gives 0.42045, which selects choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BThe value 0.29 results approximately from treating 4 as the exponential mean; the resulting five-unit survival probability is 0.2865.
CThe value 0.38 is consistent with linearly extrapolating survival rather than using the exponential time ratio.
EThe value 0.57 is the rounded failure probability 1-0.420448, not the requested survival probability.
Original practice · fully worked
Original variant: survival from a reported percentile
A router’s operating life is exponential. Its 80th percentile is 10 days, meaning 80% have failed by day 10. Find the probability a router remains operating through day 6.
A 0.2000
B 0.2759
C 0.3807
D 0.5000
E 0.7241
Variant answer in brief
Since S(10)=0.20, exponential scaling gives S(6)=0.20⁽⁶⁄¹⁰⁾=0.38073.
Setup
Setup
An 80th failure percentile at day 10 means the survival probability at day 10 is 0.20.
S(10)=0.20
S(t)=e−λt
Model
Model
For an exponential lifetime, survival at day 6 is survival at day 10 raised to the time ratio 6/10.
S(6)=(S(10))6/10
Compute
Compute
The calculation gives 0.20 to the power 0.6, equal to 0.3807308.
S(6)=0.200.6=0.3807308
Answer
Answer
The probability of remaining operational through day 6 is 0.3807, corresponding to choice C.
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