We can compute the integral directly: we have

Then the integral is



You could also take advantage of Stokes' theorem, which says the line integral of a vector field
along a closed curve
is equal to the surface integral of the curl of
over any surface
that has
as its boundary.
In this case, the underlying field is

which has curl

We can parameterize
by

with
and
.
Note that when viewed from above,
has negative orientation (a particle traveling on this path moves in a clockwise direction). Take the normal vector to
to be pointing downward, given by

Then the integral is



Both integrals are kind of tedious to compute, but personally I prefer the latter method. Either way, you end up with a value of
.
Solution:

1. For Best Actor
= 59 years

Z, Score for best actor named, 

Z-Score for best actor = 1.24
2. Z , Score for best supporting actor , called 
=49 years

Z-Score for best supporting actor = 0.70
Z-Score is usually , the number of standard deviations from the mean a point in the data set is.
3. As, 
So, we can say that,Option (B) The Best Actor was more than 1 standard deviation above is not unusual.
4.As, 
So, we can say that,Option(A) The Best Supporting Actor was less than 1 standard deviation below, is not unusual.
Answer:
Step-by-step explanation:
How many players are there?
Answer:
The shape and rate parameters are
and
.
Step-by-step explanation:
Let <em>X</em> = service time for each individual.
The average service time is, <em>β</em> = 12 minutes.
The random variable follows an Exponential distribution with parameter,
.
The service time for the next 3 customers is,
<em>Z</em> = <em>X</em>₁ + <em>X</em>₂ + <em>X</em>₃
All the <em>X</em>
's are independent Exponential random variable.
The sum of independent Exponential random variables is known as a Gamma or Erlang random variable.
The random variable <em>Z</em> follows a Gamma distribution with parameters (<em>α</em>, <em>n</em>).
The parameters are:

Thus, the shape and rate parameters are
and
.