Question

The random variable x is known to be uniformly distributed between 1.0 and 1.5. What is P (1.20≤x≤1.5)?

Answer 1

The probability that 1.20 ≤ x ≤ 1.5 in a uniform distribution is 0.6 or 60%.

Step-by-step explanation:

The random variable x follows a uniform distribution between 1.0 and 1.5. To find the probability that 1.20 ≤ x ≤ 1.5, we need to calculate the area under the curve between these two values. In a uniform distribution, the probability density function is constant.

Steps:

1. Calculate the total interval of the distribution: 1.5 - 1.0 = 0.5
2. Calculate the interval of interest: 1.5 - 1.20 = 0.30
3. Divide the interval of interest by the total interval: 0.30 / 0.5 = 0.6
   

The probability of 1.20 ≤ x ≤ 1.5 is therefore 0.6 or 60%.