Final answer:
To find the uniform continuous probability P(x < 12) for U(0, 50), calculate the area under the probability density function from 0 to 12, resulting in a probability of 0.24.
Step-by-step explanation:
To calculate the uniform continuous probability of the event P(x < 12) where x is uniformly distributed between 0 and 50 (notated as U(0, 50)), we utilize the fact that uniform distributions have equal probabilities for each interval. The probability density function, f(x), for a uniform distribution in the interval [a, b] is given by 1/(b - a). In this case, a is 0 and b is 50, so f(x) = 1/(50 - 0) = 1/50.
The probability that x is less than 12 is found by integrating the probability density function from the lower bound of the interval to the value 12. This means we calculate the area under the probability density function from x = 0 to x = 12, which is simply the rectangle's area with width 12 and height 1/50. Therefore, P(x < 12) is 12 * (1/50) = 12/50 = 0.24. Hence, the probability that x is less than 12 is 0.24.