Question

The random variable x is known to be uniformly distributed between 60 and 80. What is the probability of x having a value between 70 and 85?

1) 0.05
2) 0.75
3) 0.5
4) 1

Answer 1

The probability of x having a value between 70 and 85 is 0.75.

Step-by-step explanation:

The random variable x is uniformly distributed between 60 and 80. To find the probability of x having a value between 70 and 85, we need to find the area under the probability density function (PDF) curve between those two values.

Since the distribution is uniform, the PDF is a rectangle with height 1/(80 - 60) = 1/20 and width 20. The area of this rectangle represents the total probability of the distribution which is 1. The area of the rectangle between 70 and 85 is (85 - 70) * (1/20) = 15/20 = 0.75.

Therefore, the probability of x having a value between 70 and 85 is 0.75.