D. For the multiple choice questions, circle the best answer.

D-1) For which of the following situations would the rule for sample means not apply?

1. A random sample of size 50 is drawn from a bell- shaped population.
2. A random sample of size 20 is drawn from a skewed population.
3. A random sample of size 50 is drawn from a skewed population.
4. A random sample of size 20 is drawn from a bell- shaped population.

D-2) Which one of the following statements is false?

1. The sampling distribution of the sample mean is exactly mean is exactly normal if the observations are normally distributed.
2. The standard deviation of the sample mean decrease as the sample size increases.
3. The sampling distribution of the sample mean becomes approximately normal for large sample sizes.
4. The sampling distribution of any statistic becomes approximately normal for large sample sizes.

D-3) Which of the following statements is true about the standard deviation of X?

1. It decreases as the sample size n increases.
2. It increases as the sample size n increases.
3. It changes each time a new sample is drawn.
4. It does not change as the sample size n increases.

D-4) The standard deviation of the sampling distribution for a sample mean depends on the values of

1. neither the sample size nor the population standard deviation.
2. the population standard deviation but not the sample size.
3. the sample size and the population standard deviation.
4. the sample size but nor the population standard deviation.

D-5) For results based on a small random sample from a bell shaped distribution, the distribution of the sample mean is

1. not a bell shaped distribution.
2. approximately a normal distribution.
3. a uniform distribution
4. approximately a standard normal (z-score) distribution.

D-6) Heights for women are bell- shaped with a mean of 65 inches and standard deviation of 2.5 inches. If a random sample of 25 women is taken, what is the mean of the sampling distribution of X?

1. 65 inches
2. It depends on the value of the sample mean.
3. 2.5 inches
4. 2.5/5 = 0.5 inches

E. The distribution of house value is known to be left-skewed in the city of Wonderland in 2019, which has a mean of $700,000 with a standard deviation of $100,000.

E-1) Suppose one house in the city of Wonderland is to be randomly selected. Can we calculate the probability that this house's value is higher than $700,000? If yes, calculate is. If no, explain why not.

E-2) Suppose 100 houses in the city of Wonderland are randomly selected and the average values among them is calculated. What is the expected average house value in the sample of 100 houses?

E-3) Suppose 100 houses in the city of Wonderland are to be randomly selected and the average value in the sample is calculated. What is the standard deviation of the sampling distribution of the average house value of the 100 houses?

E-4) Suppose 100 houses in the city of Wonderland are randomly selected and the average values in the sample is calculated. What is the approximate probability that the average house value in the sample is greater than $720,000?

F. A grocery store recently changed their apple supplying vendor. The vendor told the store manager that the mean weight for each apple is bell-shaped with a mean of 8 ounces and a standard deviation of 1 ounce.

F-1) One customer comes to this grocery store and randomly picks 6 apples. What is the mean and standard deviation of the distribution of the mean weight for 6 apples?

F-2) What is the probability that the mean weight of 6 apples exceeds 9 ounces?