Question

If you have a random variable X that represents a normal distribution with mean (µ) and standard deviation (σ). As n increases in random samples of size n, the random variable Ȳ (sample means) tends to be normally distributed and can be represented by:

a. Ȳ = X - µ / σ√n
b. Ȳ = X - µ / σ
c. Ȳ = X - µ / √n
d. Ȳ = X - µ / σ√n

Answer 1

The formula to represent the sample means is Ȳ = X - µ / σ√n. Option d. Ȳ = X - µ / σ√n correctly represents the relation between the random variable Ȳ and the mean (µ) and standard deviation (σ).

Step-by-step explanation:

The sampling distribution of the mean for random samples of size n tends to be normally distributed as n increases. The formula to represent the sample means is Ȳ = X - µ / σ√n.

Option d. Ȳ = X - µ / σ√n correctly represents the relation between the random variable Ȳ and the mean (µ) and standard deviation (σ).