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For this uniform distribution, the shape of the density function is a line. We can begin by identifying key elements of the distribution:
Range: 6 to 14 pounds
Formula of density function:
y = 1/Range
1 - (14 - 6) = 1/8 = 0.125
f(x) = 0.125
1)
P(x = 7)
A uniform distribution is a continuous distribution, so the probability of x being an EXACT value is approximately 0.
<u>This is the same as if we took the following integral. (Finding the area under a curve with the same start and end point)</u>
Therefore, P(x = 7) = 0.
2)
We can think of this as finding the area of a rectangle.
The width would be the difference between 8.25 pounds and 12 pounds:
W = 12 - 8.25 = 3.75
The height would be the function (y = .125), or:
h = .125
Using the equation for the area of a rectangle: (A = h * w)
A = 3.75 * .125 = 0.469
Thus, P(8.25 < x < 12) = 0.469
3)
To find the probability GREATER than 10.50 pounds, we can subtract this value from the max value for the width:
W = 14 - 10.50 = 3.50
The height is the same as above:
h = .125
Solve for the area:
A = 3.50 * .125 = 0.4375
P(x > 10.5) = 0.4375
For this case we must simplify the following expression:
We must add similar terms taking into account that:
- Equal signs are added and the same sign is placed.
- Different signs are subtracted and the major sign is placed.
Thus, the simplified expression is:
Answer:
The number of possible seats is an illustration of permutation
There are 1728 possible sitting arrangements
<h3>How to determine the number of seats</h3>From the question, we have the following highlights:
- Chris can only take 1 seat (i.e. the central seat)
- Jo can take 2 seats (i.e. the seats adjacent the central seat)
- Alex, Barb and Dave can take 3! number of seats
- Eddie, Fred, and Gareth can take 3! number of seats on the right of Chris.
- The remaining 4 adults do not have preference, then they can seat in 4! ways
So, the number of sitting arrangement is:
Evaluate the product
Hence, there are 1728 possible sitting arrangements
Read more about permutation at: