I have a couple of questions that need review--I've answered them, but I'm not sure if I'm correct.

1.)Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents:

a) the bias, if any, which is present in the sampling method

b)the true population average commute distance

c)simple random sample

d)the sampling distribution of the sample mean

I chose choice "d" but I was torn between that and choice "b"

2)The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed.

We know the random variable has approximately a normal distribution because of
Choose one answer.

a. the central limit theorem.

b. the law of large numbers.

c. the 68–95–99.7 rule.

d. the population we're sampling from has a Normal distribution.

I chose choice "a"

Looks OK!

1) The correct answer is d) the sampling distribution of the sample mean.

Explanation:
When you repeat the survey many times and record different sample mean commute distances, you are essentially creating a distribution of those sample means. This distribution is called the sampling distribution of the sample mean. It shows the variability in the sample mean commute distances that you might expect to see if you were to repeat the survey many times. This distribution provides information about the spread and shape of the sample means. It's important to note that the sampling distribution of the sample mean is different from the true population average commute distance (option b). The sampling distribution represents the variability due to random sampling, while the true population average represents the actual average commute distance of the population.

2) The correct answer is a) the central limit theorem.

Explanation:
The central limit theorem states that when independent random samples are taken from any population, regardless of its shape, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. In this case, the random variable is the sample mean age of the residents in the retirement community. Since the sample size is large (100), we can apply the central limit theorem and conclude that the distribution of the sample mean age will be approximately normal. The central limit theorem allows us to make inferences and perform statistical analysis assuming normality, even if the population from which we sample does not follow a normal distribution.