PLEASE I NEED HELP WITH THE DISTRIBUTION OF SAMPLES PROBLEM

(1) The average production cost for major movies is 58 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 44 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 of X? X ~ N(Correct,Correct)
2. What is the distribution of x? x ~ N(Correct,)
3. For a single randomly selected movie, find the probability that this movie's production cost is between 56 and 62 million dollars. Correct
4. For the group of 44 movies, find the probability that the average production cost is between 56 and 62 million dollars. Correct
5. For part d), is the assumption of normal necessary? YesNo

(2) The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 20. Suppose that 13 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 63.9 and 67.5.
4. For the 13 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 63.9 and 67.5.
5. For part d), is the assumption that the distribution is normal necessary? YesNo

(3) Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 2 month. 35 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 10.7 and 11.5 months old?
4. For the 35 people, find the probability that the average age that they learned to walk is between 10.7 and 11.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? NoYes
6. Find the IQR for the average first time walking age for groups of 35 people. Q1 = months Q3 = months IQR: months

(4) The lengths of adult males' hands are normally distributed with mean 195 mm and standard deviation is 7.4 mm. Suppose that 6 individuals are randomly chosen. Round all answers to 4 where possible.

1. What is the distribution of x? x ~ N(Correct,)
2. For the group of 6, find the probability that the average hand length is more than 191. Correct
3. Find the first quartile for the average adult male hand length for this sample size.
4. For part b), is the assumption that the distribution is normal necessary? NoYes

(5) Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 42 minutes and standard deviation 21 minutes. A researcher observed 9 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N(Correct,Correct)
2. What is the distribution of x? x ~ N(Correct,)
3. What is the distribution of x? x ~ N(Correct,)
4. If one randomly selected student is timed, find the probability that this student's time will be between 38 and 48 minutes.
5. For the 9 students, find the probability that their average time studying is between 38 and 48 minutes. Correct
6. Find the probability that the randomly selected 9 students will have a total study time less than 297 minutes.

(6) The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.3 minutes. 45 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N(Correct,Correct)
2. What is the distribution of x? x ~ N(Correct,)
3. What is the distribution of x? x ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.4856 and 23.8856 minutes. Correct
5. For the 45 runners, find the probability that their average time is between 23.4856 and 23.8856 minutes.
6. Find the probability that the randomly selected 45 person team will have a total time more than 1102.5.