Question

Let X a random variable with a uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the standard deviation of X.

a. 2.1547
b. 1.1547
c. 3.1547

Answer 1

The standard deviation of a uniform distribution with a minimum of 6 and a maximum of 10 is 1.1547 (option b), calculated using the formula for the standard deviation of a uniform distribution.

Step-by-step explanation:

To find the standard deviation of a uniform distribution, we use the formula σ = (b - a) / √12, where a is the minimum value, b is the maximum value, and σ represents the standard deviation.


In this case, the random variable X has a uniform distribution with a minimum value of 6 and a maximum value of 10.

Applying the formula:

• a = 6
• b = 10

The standard deviation (σ) is therefore calculated as follows:

σ = (10 - 6) / √12


σ = 4 / √12


σ = 4 / 3.464


σ = 1.1547

Thus, the standard deviation of X is 1.1547, which corresponds to option b.