Question

if the number of degrees of freedom for a chi-square distribution is 10, what is the population standard deviation?

Answer 1

The population standard deviation (σ) for a chi-square distribution with 10 degrees of freedom is approximately 4.47.

Step-by-step explanation:

The population standard deviation (σ) for a chi-square distribution can be calculated using the formula:

σ = √(2 * df)

Given that the number of degrees of freedom (df) is 10, we can substitute it into the formula to find the population standard deviation:

σ = √(2 * 10) = √20 ≈ 4.47

Therefore, the population standard deviation for a chi-square distribution with 10 degrees of freedom is approximately 4.47.

Answer 2

The population standard deviation for a chi-square distribution with 10 degrees of freedom is approximately 4.471.

The population standard deviation for a chi-square distribution is calculated using the formula:

Population standard deviation=√2×degrees of freedom

Given the degrees of freedom (df) as 10, let's substitute it into the formula:

Population standard deviation=√2 × 10

=√20

To simplify this further:

=√4 × 5

= √4 × √5

=2 × √5

Therefore, the population standard deviation for a chi-square distribution with 10 degrees of freedom is 2 × √5 which is approximately 4.47 when rounded to two decimal places. This calculation is based on the formula that utilizes the number of degrees of freedom in the chi-square distribution to find the population standard deviation.