The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is?

Solution;

Given the random variable x is known to be uniformly distributed between 70 and 90.

For uniform distribution, the probability is computed by applying the formula of the area of a rectangle.

We know the area of rectangle is given as

Area = Width⋅Height

According to the uniform probability density function,

f(x) = 1/(b - a) where, a denotes the minimum value and b denotes the maximum value.

From the information given, a = 70,b = 90. i.e., x is distributed between 70 and 90

Thus the height is computed as shown below:

Height = 1/(90 - 70) = 1/20

It is required to find the probability of the uniform random variable to be within 80 and 95 respectively. Thus width is computed as shown below:

Width = 95 - 80 = 15

Therefore, the required probability is obtained by computing the area as shown below:

Area = Width⋅Height = 15(1/20) = 0.75

---

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is?

Summary:

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is 0.75