Answer:
- P(X<16) = 0.64
- P(X>12) = 0.64
Explanation:
Given a graph of a probability density function, you want the probabilities ...
Probability from PDF
The probability of a given range of values of X is the area under the density curve for those values of x.
P(X < 16)
The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:
A = 1/2bh
A = 1/2(16)(0.08) = 0.64
The probability is P(X<16) = 0.64.
P(X > 12)
The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(0.06 +0.10)(8) = 0.64
The probability is P(X>12) = 0.64.