Question

Suppose ( x ) is a uniform random variable with values ranging from 10 to 80. Find the probability that a randomly selected observation is between 13 and 75.

A. {3} / {4}
B. {2} / {3}
C. {5} / {6}
D. {3} / {5}

Answer 1

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.