Using the standard normal table, the probability that Seth’s light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is abo
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The Jacobian for this transformation is
with determinant , hence the area element becomes
Then the integral becomes
where is the unit circle,
so that
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
Then