Final Answer:
The probability that a randomly selected observation is between 13 and 75, for a uniform random variable with values ranging from 10 to 80, is 3/4.
Step-by-step explanation:
Given a uniform random variable x with values between 10 and 80.
The probability density function for a uniform distribution is f(x) = 1/(b-a), where a and b are the lower and upper bounds.
Calculate the probability for the interval [13, 75]:
Probability P(13 ≤ x ≤ 75) = 1/(80-10) × (75-13) = 3/4.
Compare the result with the given options:
A. 3/4 matches the calculated probability.
B. 2/3 does not match.
C. 5/6 does not match.
D. 3/5 does not match.
The correct probability is 3/4.