Question

Is the following inequality sometimes, always, or never true?

a) Sometimes, when x is less than 12
b) Sometimes, when x is greater than 12
c) Sometimes, when x is less than 9
d) Always true
e) Never true

Answer 1

The probability P (0 < x < 12) of a continuous probability function that is equal to 12 and restricted to 0 ≤ x ≤ 12 is always 100%, since the function covers the entire interval with a constant value.

Step-by-step explanation:

The question seems to refer to an inequality, but the actual inequality is not provided. However, based on the additional context given, we can discuss the continuity and probability of a function over an interval.

If we have a continuous probability function f(x) that is equal to 12 over the interval from 0 to 12, we can determine the probability P of x being between 0 and 12. Since the function is constant and the interval is the entire domain of the function, the probability P (0 < x < 12) is 100%.

This is because the probability distribution accounts for all possible values of x within the domain, and there are no values of x outside this interval. In other words, it is always true that the probability is 1 (or 100%) since f(x) is defined and constant over the entire specified domain.