1, The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.4 minutes. 15 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 ofXX?XX~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. What is the distribution ofxx?xx~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.8704 and 24.4704 minutes.
5. For the 15 runners, find the probability that their average time is between 23.8704 and 24.4704 minutes.
6. Find the probability that the randomly selected 15 person team will have a total time less than 366.
7. For part e) and f), is the assumption of normal necessary?NoYes
8. The top 20% of all 15 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round?minutes

2, Each sweat shop worker at a computer factory can put together 4.2 computers per hour on average with a standard deviation of 0.9 computers. 49 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 and 4.1 computers per hour.
5. For the 49 workers, find the probability that their average number of computers put together per hour is between 4 and 4.1.
6. Find the probability that a 49 person shift will put together between 196 and 200.9 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 49 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker?minutes (round to the nearest computer)

3, Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 23 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 47 and 51 minutes.
5. For the 17 students, find the probability that their average time studying is between 47 and 51 minutes.
6. Find the probability that the randomly selected 17 students will have a total study time less than 884 minutes.
7. For part e) and f), is the assumption of normal necessary?NoYes
8. The top 20% 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

4, The average amount of money that people spend at Don Mcalds fast food place is $7.0600 with a standard deviation of $1.9100. 12 customers are randomly selected. Please answer the following questions, and 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. What is the probability that one randomly selected customer will spend less than $7.1129?
5. For the 12 customers, find the probability that their average spent is more than $7.1129.
6. Find the probability that the randomly selected 12 customers will spend less than $85.3548.
7. For part e) and f), is the assumption of normal necessary?YesNo
8. The owner of Don Mcalds gives a coupon for a free sundae to the 4% of all groups of 12 people who spend the most money. At least how much must a group of 12 spend in total to get the free sundae? $

5, The average score for games played in the NFL is 21.2 and the standard deviation is 9.3 points. 15 games are randomly selected. 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. P(xx> 19.0982) =
4. Find the 70th percentile for the mean score for this sample size.
5. P(18.6982
6. Q1 for thexxdistribution =
7. P(xx> 328.473) =
8. For part c) and e), is the assumption of normal necessary?NoYes