1. The average production cost for major movies is 57 milliondollars and the standard deviation is 22 million dollars. Assumethe production cost distribution is normal. Suppose that 46randomly selected major movies are researched. Answer the followingquestions. Round all answers to 4 decimal places wherepossible.

1. What is the distribution of X? X~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. For a single randomly selected movie, find the probability thatthis movie's production cost is between 51 and 56 milliondollars.
4. For the group of 46 movies, find the probability that theaverage production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normallydistributed with mean 11 months and standard deviation 1.1 month.18 randomly selected people were asked what age they learned towalk. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )  
2. What is the distribution of x¯? x¯ ~ N( , )
3. What is the probability that one randomly selected personlearned to walk when the person was between 10 and 12.5 monthsold?
4. For the 18 people, find the probability that the average agethat they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normalnecessary? Yes or No
6. Find the IQR for the average first time walking age for groupsof 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tirewill function before needing replacement is 72 and the standarddeviation is 12. Suppose that 8 randomly selected tires are tested.Round all answers to 4 decimal places where possible and assume anormal distribution.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a randomly selected individual tire is tested, find theprobability that the number of miles (in thousands) before it willneed replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the averagemiles (in thousands) before need of replacement is between 78.2 and84.2.

4. The lengths of adult males' hands are normally distributedwith mean 188 mm and standard deviation is 7.2 mm. Suppose that 17individuals are randomly chosen. Round all answers to 4 decimalplaces where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 17, find the probability that the average handlength is more than 187.
3. Find the third quartile for the average adult male hand lengthfor this sample size.

5. Suppose that the average number of Facebook friends usershave is normally distributed with a mean of 125 and a standarddeviation of about 55. Assume fourteen individuals are randomlychosen. Answer the following questions. Round all answers to 4decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 14, find the probability that the averagenumber of friends is less than 107.
3. Find the first quartile for the average number of Facebookfriends

6. The amount of syrup that people put on their pancakes isnormally distributed with mean 57 mL and standard deviation 9 mL.Suppose that 41 randomly selected people are observed pouring syrupon their pancakes. Round all answers to 4 decimal places wherepossible.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a single randomly selected individual is observed, find theprobability that this person consumes is between 57.7 mL and 59.2mL.
4. For the group of 41 pancake eaters, find the probability thatthe average amount of syrup is between 57.7 mL and 59.2 mL