Final answer:
To find f(2) for the function f(n) = 12n, we substitute n with 2 and calculate f(2) to get 24. For the probability function f(x) = 12, where 0 ≤ x ≤ 12, the probability that x is between 0 and 12 is 1 or 100%, since the function's value multiplied by the interval's length equals 144 and needs to be normalized to a total probability of 1.
Step-by-step explanation:
To find f(2) for the function f(n) = 12n, we simply substitute the value of n with 2. Calculating f(2), we get:
f(2) = 12 × 2 = 24
Therefore, f(2) is 24.
Regarding the probability question, if f(x) is a continuous probability function that is constant and equal to 12 on the interval 0 ≤ x ≤ 12, then the probability P for 0 < x < 12 is essentially the area under the curve from 0 to 12. Since the function is constant, we can calculate the area by multiplying the function value (12) by the length of the interval (12), which results in: P(0 < x < 12) = 12 × 12 = 144.
However, since it is a probability function, the total area under the curve must be 1 (or 100%). Therefore, the area of 144 must be normalized. We do this by dividing by the total possible probability area, which is also 144, resulting in:
P(0 < x < 12) = 144/144 = 1
This means that the probability is 1 or 100% that the value of x will fall between 0 and 12.