Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. a. What’s the probability density function?
b. What’s the probability that X will take on a value between 21 and 25?
c. What’s the probability that X will take on a value of at least 26?

a) The probability distribution is

b) 0.5 = 50% probability that X will take on a value between 21 and 25.

c) 0.25 = 25% probability that X will take on a value of at least 26.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

The probability of finding a value between c and d is:

The probability of finding a value above x is:

Uniform distribution over the interval from 20 to 28.

This means that

a. What’s the probability density function?

The probability density function of the uniform distribution is:

In this question:

b. What’s the probability that X will take on a value between 21 and 25?

0.5 = 50% probability that X will take on a value between 21 and 25.

c. What’s the probability that X will take on a value of at least 26?

0.25 = 25% probability that X will take on a value of at least 26.

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step-by-step explanation: