Question

If the number of degrees of freedom for a chi-square distribution is 20, what is the population mean and standard deviation?

a. The population mean is 20, and standard deviation is 4.47.
b. The population mean is 20, and standard deviation is 40.
c. The population mean is 20, and standard deviation is 6.32.
d. The population mean is 19, and standard deviation is 19.

Answer 1

The chi-square distribution with 20 degrees of freedom has a population mean of 20 and a standard deviation of approximately 6.32. The correct answer is option (c), which provides these exact values.

Step-by-step explanation:

The chi-square distribution with 20 degrees of freedom will have a population mean (µ) equal to the number of degrees of freedom, and a standard deviation (σ) equal to the square root of twice the degrees of freedom. Calculating the standard deviation:

1. Find the degrees of freedom (df): 20.
2. Calculate the standard deviation (σ): σ = √2(df) = √2(20) = √40 ≈ 6.32.

Thus, the correct answer is (c) - the population mean is 20, and standard deviation is 6.32.