To solve, use the distance formula: 
. Using your values of x and y, you get 
, which is approximately 9.22. This means your shortest distance is √85≈9.22
in a certain normal distribution, 6.3% of the area lies to the left of 36 and 6.3% of the area lies to the right of 42. Find the
1 answer:
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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
.
From the diagram, we can see that the radius of the cone is 8cm and the height of the cone is 15cm. We then just plug these numbers into the formula and simplify:
The volume of the cone is approximately 1005.3096 cm^3. With 3 sig figs, this is 1010 cm^3.