The central limit theorem states that when a sample was chosen with simple random sampling and its size is greater than or equal to 30 then the sampling distribution of the sample is approximately normal.  True or

A random variable is normally distributed. It has a mean of 283 and a standard deviation of 21. If you take a sample of size 14, can you say what the shape of the sampling distribution for the sample mean is? Why? If the sample size is 14, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30. O If the sample size is 14, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed. If the sample size is 14, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30. For a sample of size 14, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. Hx= 0x = For a sample of size 14, find the probability that the sample mean is more than 280. P(x > 280) = If…

A simple random sample of size n=10 is obtained from a population that is normally distributed with a mean of 40 and a standard deviation of 3. Is the sampling distribution normally distributed? Why? Yes, the sampling distribution is normally distributed because the population is normally distributed. Yes, the sampling distribution is normally distributed because the population mean is greater than 30. No, the sampling distribution is not normally distributed because the population is not normally distributed. No, the sampling distribution is not normally distributed because the sample size is less than 30.

Suppose that 70% of residents in a certain city own at least one pet. You select a random sample of 30 city residents. Let X = the number of residents that own at least one pet. Would it be appropriate to use a normal distribution to model the sampling distribution of X? No, there are at least 10 "successes" expected, but there are not at least 10 "failures" expected. It is not appropriate to use a normal distribution to model the sampling distribution of X. No, the sample size is greater than 10, so it is not appropriate to use a normal distribution to model the sampling distribution of X. Yes, the sample size is at least 30, so it is appropriate to use a normal dist bution to model the sampling distr ution of X. Yes, there are at least 10 "successes" expected and 10 "failures" expected so it is appropriate to use a normal distribution to model the sampling distribution of X. No, there are not at least 10 "successes" expected, although there are at least 10 "failures" expected. It is…