The time it takes Jessica to bicycle to school is normally distributed with mean 15 minutes and variance 4. Jessica has to be at
1 answer:
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Make a change of coordinates:
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
to 
. To do this, notice that
we need to take the reciprocal of the Jacobian above.
The integral then changes to
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
we need to take the reciprocal of the Jacobian above.
The integral then changes to
So for this, we can simplify √63 as such:
Using the simplified version of √63, we can solve it:
Zero is your final answer.