(b) Compute P(x < 35). When dealing with continuous distributions, the probability will be for a range of values instead of a single value. This probability will be the area under the graph between the given values. For a = 30 and b = 40, the height of the density function was found to be 0.10. This gives the following uniform probability density distribution. 1 f(x) = b-a a≤x≤b elsewhere 0 = 0.10 0 30 ≤ x ≤ 40 elsewhere The graph of this distribution is a rectangle, which has an area equal to the width multiplied by the height. The height was found to be 0.10, so the width is needed. Since the desired probability is that x < 35, and this distribution is only valid when x is between 30 and 40, the rectangle representing this probability will be between ---Select--- giving a width of . Find the area of this rectangle, which is also P(x < 35). P(x < 35) = width height (0.10)

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(b) Compute P(x < 35).
When dealing with continuous distributions, the probability will be for a range of values instead of a single value. This probability will be the area under the graph between the given
values. For a = 30 and b = 40, the height of the density function was found to be 0.10. This gives the following uniform probability density distribution.
1
a ≤x≤ b
f(x)
=
0
elsewhere
0.10
30 ≤ x ≤ 40
0
elsewhere
The graph of this distribution is a rectangle, which has an area equal to the width multiplied by the height. The height was found to be 0.10, so the width is needed.
Since the desired probability is that x < 35, and this distribution is only valid when x is between 30 and 40, the rectangle representing this probability will be between |---Select---
giving a width of
Find the area of this rectangle, which is also P(x < 35).
P(x < 35) = width height
=
|)(0.10)
=
b
a
Transcribed Image Text:(b) Compute P(x < 35). When dealing with continuous distributions, the probability will be for a range of values instead of a single value. This probability will be the area under the graph between the given values. For a = 30 and b = 40, the height of the density function was found to be 0.10. This gives the following uniform probability density distribution. 1 a ≤x≤ b f(x) = 0 elsewhere 0.10 30 ≤ x ≤ 40 0 elsewhere The graph of this distribution is a rectangle, which has an area equal to the width multiplied by the height. The height was found to be 0.10, so the width is needed. Since the desired probability is that x < 35, and this distribution is only valid when x is between 30 and 40, the rectangle representing this probability will be between |---Select--- giving a width of Find the area of this rectangle, which is also P(x < 35). P(x < 35) = width height = |)(0.10) = b a
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