A zircon semiconductor is critical to the operation of a superconductor and must be replaced immediately upon failure. Its expected lifetime is 100 hrs and stan- dard deviation is 34 hrs. If 22 of...

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A zircon semiconductor is critical to the operation of a superconductor and must
be replaced immediately upon failure. Its expected lifetime is 100 hrs and stan-
dard deviation is 34 hrs. If 22 of these semiconductors are available, approximate
the probability that the superconductor can operate can operate for at least 2000 hrs.

Answered Same DayDec 26, 2021

Answer To: A zircon semiconductor is critical to the operation of a superconductor and must be replaced...

Robert answered on Dec 26 2021
132 Votes
Total of 22 is more than 2000 is equivalent to average of 22 is more than
2000/22 = 90.909091
P (X ≥ 90.909091)
We can calculate this because of normal approximation of sampling distribution
as per central limit theorem.
Normal Distribution, µ = 100, σ = 34, n = 22
Since this is continuous distribution, P (X ≥ 90.909091) = P (X > 90.909091)
we convert this to standard normal using z = x− µx
σx
= x− µ
σ/
√
n
z = 90.909091−...
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