Final answer:
The probability that a uniformly distributed random variable x over the interval [40, 50] exceeds 43 is 0.7, or 70%, as it's based on the length of the interval from 43 to 50 compared to the entire interval.
Step-by-step explanation:
To find the probability that a randomly selected observation from a uniform random variable x over the interval [40, 50] exceeds 43, we need to utilize the properties of a uniform distribution. Since the variable is uniformly distributed, the probability is proportional to the length of the interval in which the observation falls. Therefore, the probability that x is greater than 43 is equal to the proportion of the interval from 43 to 50 relative to the entire interval from 40 to 50.
First, calculate the length of the interval from 43 to 50, which is 50 - 43 = 7. Next, calculate the total length of the interval from 40 to 50, which is 50 - 40 = 10. The probability is then P(x > 43) = (7/10).
Therefore, P(x > 43) = 0.7 or 70%.