1, The average price of a college math textbook is $160 and the standard deviation is $22. Suppose that 15 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 15, find the probability that the average price is between $154 and $157.
3. Find the third 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?NoYes

2, The amount of syrup that people put on their pancakes is normally distributed with mean 58 mL and standard deviation 12 mL. Suppose that 46 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution ofXX?XX~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 58 mL and 59.8 mL.
4. For the group of 46 pancake eaters, find the probability that the average amount of syrup is between 58 mL and 59.8 mL.
5. For part d), is the assumption that the distribution is normal necessary?NoYes

3, The average amount of money spent for lunch per person in the college cafeteria is $6.14 and the standard deviation is $2.9. Suppose that 40 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 ofXX?XX~ 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 $6.5623 and $7.0916.
4. For the group of 40 patrons, find the probability that the average lunch cost is between $6.5623 and $7.0916.
5. For part d), is the assumption that the distribution is normal necessary?NoYes

4, The average production cost for major movies is 63 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 40 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 ofXX?XX~ 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 60 and 66 million dollars.
4. For the group of 40 movies, find the probability that the average production cost is between 60 and 66 million dollars.
5. For part d), is the assumption of normal necessary?NoYes

5, Each sweat shop worker at a computer factory can put together 4.3 computers per hour on average with a standard deviation of 0.8 computers. 15 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution ofXX?XX~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. What is the distribution ofxx?xx~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.1 and 4.4 computers per hour.
5. For the 15 workers, find the probability that their average number of computers put together per hour is between 4.1 and 4.4.
6. Find the probability that a 15 person shift will put together between 61.5 and 63 computers per hour.
7. For part e) and f), is the assumption of normal necessary?YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 15 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker?minutes (round to the nearest computer)

6, Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 50 minutes and standard deviation 20 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution ofXX?XX~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. What is the distribution ofxx?xx~ N(,)
4. If one randomly selected student is timed, find the probability that this student's time will be between 48 and 52 minutes.
5. For the 17 students, find the probability that their average time studying is between 48 and 52 minutes.
6. Find the probability that the randomly selected 17 students will have a total study time more than 782 minutes.
7. For part e) and f), is the assumption of normal necessary?YesNo
8. The top 10% of the total study time for groups of 17 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker?minutes

7, A computer selects a numberXXfrom 0 to 5 randomly and uniformly. Round all answers to 4 decimal places where possible.

1. What is the distribution ofXX?XX~ U(,)
2. Suppose that the computer randomly picks 36 such numbers.What is the distribution ofxxfor this selection of numbers.xx~ N(,)
3. What is the probability that the average of 36 numbers will be more than 2.3?