Question

1. The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. 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. For a single randomly selected movie, find the probability that this movie's production cost is between 51 and 56 million dollars.
4. For the group of 46 movies, find the probability that the average production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. 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 person learned to walk when the person was between 10 and 12.5 months old?
4. For the 18 people, find the probability that the average age that they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No
6. Find the IQR for the average first time walking age for groups of 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal 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 the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2.

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

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

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

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

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. 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. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL.
4. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL

Answer 1