Looks like we're given
which in three dimensions could be expressed as
and this has curl
which confirms the two-dimensional curl is 0.
It also looks like the region is the disk
. Green's theorem says the integral of
along the boundary of
is equal to the integral of the two-dimensional curl of
over the interior of
:
which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of by
with . Then
Answer:
The probability that x equals 19.62 is 0
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In the normal probability distribution, the probability of an exact value, that is, P(X = x) is 0. Thus, the probability that x equals 19.62 is 0