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
.
If a light bulb consumes 600 per day, then you need to divide 2250 by 600. So it would be around 3.75 days
The avarage is 180:18=10 , 10 min per hole
I set it in a big problem. Since you know that all the angles of a triable add up to 180,
m<a + m<b + m<c = 180, plug in equations/values
(36) + (3x+12) + (3x+18) = 180, subtract 36
3x+12 + 3x+18 = 144, combine like terms,
6x+30 = 144, subtract 30,
6x=114, divide by 6,
x=19. Plug in X to the equations for m<b and m<c