(09.02)
1 answer:
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Hello!
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
Answer:
(a) [8, 14]
(b)
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:
Solving the absolute inequality
(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.
