Suppose f(x)= 1/4 over the range a ≤ x ≤ b,and suppose P(X 4)= 1/2.What are the values for a and b?
A)0 and 4
B)2 and 6
C)Can be any range of x values whose length (b − a)equals 4.
D)Cannot answer with the information given.

Question

Suppose f(x)= 1/4 over the range a ≤ x ≤ b,and suppose P(X > 4)= 1/2.What are the values for a and b?
A)0 and 4
B)2 and 6
C)Can be any range of x values whose length (b − a)equals 4.
D)Cannot answer with the information given.

Quizplus · Accepted Answer

Since P(X > 4) = 1/2, this means that half of the total area under the curve lies to the right of x = 4. Since the given function f(x) is constant over the range a ≤ x ≤ b, the total area under the curve can be written as:
total area = f(x) * (b - a) = 1/4 * (b - a)
Half of this area lies to the right of x = 4, so we can write:
1/2 = (1/4) * (b - 4)
Solving for b, we get:
b = 2 + 4 = 6
Similarly, half of the total area lies to the left of x = 2. So we can write:
1/2 = (1/4) * (2 - a)
Solving for a, we get:
a = 2 - 2 = 0
Therefore, the values for a and b are a=0 and b=6, which corresponds to choice B.

Suppose F(x)= 1/4 Over the Range a ≤ X ≤