Question 1

Which of the following is true about the sampling distribution of means?

• Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.
• Sampling distributions of means are always nearly normal.
• Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.
• Sampling distributions of means get closer to normality as the sample size increases.

Question 2

The population mean will always be the same as the mean of all possibleXXthat can be computed from samples of size 37.

• True
• False

Question 3

If the sample size is 36 and the population standard deviation is 30, then the standard deviation of the sampling distribution for means is 5.

• True
• False

Question 4

The symbolxxrepresents the population mean of all possible sample means of size n.

• False
• True

Question 5

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 100-cm and a standard deviation of 2.3-cm. For shipment, 49 steel rods are bundled together.Round all answers to four decimal places if necessary.

1. What is the distribution ofX?X~ N
2. What is the distribution ofxx?xx~ N
3. For a single randomly selected steel rod, find the probability that the length is between 99.5-cm and 99.7-cm.
4. For a bundled of 49 rods, find the probability that the average length is between 99.5-cm and 99.7-cm.
5. For part d), is the assumption of normal necessary? Yes or No

Question 6

The average amount of money spent for lunch per person in the college cafeteria is $6.94 and the standard deviation is $2.35. Suppose that 50 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

1. What is the distribution of X?X~ N
2. What is the distribution ofxx?xx~ N
3. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.2416 and $7.5378.
4. For the group of 50 patrons, find the probability that the average lunch cost is between $7.2416 and $7.5378.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No

Question 7

The average production cost for major movies is 64 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 35 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible.

1. What is the distribution ofX?X~ N
2. What is the distribution ofxx?xx~ N
3. For a single randomly selected movie, find the probability that this movie's production cost is between 66 and 68 million dollars.
4. For the group of 35 movies, find the probability that the average production cost is between 66 and 68 million dollars.
5. For part d), is the assumption of normal necessary? No or Yes

Question 8

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.7 ppm and standard deviation 1.4 ppm. 13 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

1. What is the distribution ofX?X~ N
2. What is the distribution ofxx?xx~ N
3. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
4. For the 13 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
5. For part d), is the assumption that the distribution is normal necessary? No or Yes
6. Find the IQR for the average of 13 cities. Q1 = ppm Q3 = ppm IQR: ppm

Question 9

The average price of a college math textbook is $158 and the standard deviation is $20. Suppose that 9 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution ofxx?xx~ N
2. For the group of 9, find the probability that the average price is between $161 and $166.
3. Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
4. For part b), is the assumption that the distribution is normal necessary? No orYes

Question 10

The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces and a standard deviation of 4.5 ounces. 10 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

1. What is the distribution ofX?X~ N
2. What is the distribution ofxx?xx~ N
3. What is the probability that one randomly selected person drinks between 14 and 16 ounces of coffee per day?
4. For the 10 people, find the probability that the average coffee consumption is between 14 and 16 ounces of coffee per day.
5. For part d), is the assumption that the distribution is normal necessary? Yes orNo
6. Find the IQR for the average of 10 coffee drinkers. Q1 = ounces Q3 = ounces IQR: ounces