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
.
Answer: 100
Step-by-step explanation:
Given : The total number of seats planned in new restaurant =134
The percentage of customers demand a smoke-free area = 62%
It can also be written as 
The mean of this binomial distribution will be :-

Standard deviation:-

Now, the number of seats should be in the non-smoking area in order to be very sure of having enough seating there :-

Formula for area of parallelogram:
A= bh
Where b is the length of base and h is the height.
Here b=2.3+4.5 = 6.8 cm
and h= 4.5 cm
Put values in formula.
A= 6.8 x 4.5
A=30.6 cm²
Answer: 30.6 cm²
The number of patches that Leia can cut from 32 pieces of the fabric measuring 18 cm by 10 cm will be as follows:
Number of pieces=[total area of fabric]/[area of patch]
area of fabric=18×10=180 cm²
Area of 32 patches=180×32=5760 cm²
Area of patch=45 cm²
Number of patches=5760/45=128 patches
D1 = 60 for a price of $80. Charging $80 will ensure supply exceeds demand.
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The store apparently could charge a price slightly lower than $80, but we cannot tell from the chart how much lower.