Chapter 7, Problem 9CR

Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means $\bar{x}$.

As the sample size becomes increasingly large, what distribution does the $\bar{x}$ distribution approach?

As the sample size becomes increasingly large, what value will the mean ${\mu }_{\bar{x}}$ of the $\bar{x}$ distribution approach?

What value will the standard deviation $\sigma \bar{x}$ of the sampling distribution approach?

How do the two $\bar{x}$ distributions for sample size n = 50 and n = 100 compare?