1.- The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 minutes. 6 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution ofX?X ~ N(________,________)

b. What is the distribution ofx?x ~ N(,)

c. What is the distribution ofx?x~ N(________,_________)

d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.4465 and 22.3465 minutes.______________

e. For the 6 runners, find the probability that their average time is between 21.4465 and 22.3465 minutes.____________

f. Find the probability that the randomly selected 6 person team will have a total time more than 127.2._________

g. For part e) and f), is the assumption of normal necessary?No or Yes_________

h. The top 10% of all 6 person team relay races will compete in the championship round. These are the 10% 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 4.7 computers per hour on average with a standard deviation of 0.9 computers. 7 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.

a. What is the distribution ofX?X~ N(________,________)

b. What is the distribution ofx?x ~ N(_______,_______)

c. What is the distribution ofx?x~ N(_________,__________)

d. if one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.6 computers per hour.___________

e. For the 7 workers, find the probability that their average number of computers put together per hour is between 4.4 and 4.6._____________

f. Find the probability that a 7 person shift will put together between 30.1 and 32.9 computers per hour.______________

g. For part e) and f), is the assumption of normal necessary?No or Yes_________

h. A sticker that says "Great Dedication" will be given to the groups of 7 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 43 minutes and standard deviation 23 minutes. A researcher observed 46 students who entered the library to study. Round all answers to 4 decimal places where possible.

a. What is the distribution ofX?X ~ N(________,_________)

b. What is the distribution ofx?x~ N(_________,_________)

c. What is the distribution ofx?x ~ N(__________,_________)

d. If one randomly selected student is timed, find the probability that this student's time will be between 45 and 48 minutes._______________

e. For the 46 students, find the probability that their average time studying is between 45 and 48 minutes._____________

f. Find the probability that the randomly selected 46 students will have a total study time less than 2116 minutes.______________

g. For part e) and f), is the assumption of normal necessary?Yes or No______________

h. The top 20% of the total study time for groups of 46 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 $7.8300 with a standard deviation of $1.7800. 14 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution ofX?X~ N(_________,_________)

b. What is the distribution ofx?x~ N(__________,__________)

c. What is the distribution ofx?x~ N(_________,_________)

d. What is the probability that one randomly selected customer will spend less than

$8.2765?___________________

e. For the 14 customers, find the probability that their average spent is more than

$8.2765.____________

f. Find the probability that the randomly selected 14 customers will spend more than

$115.8710.___________________

g. For part e) and f), is the assumption of normal necessary?Yes or No___________

h. The owner of Don Mcalds gives a coupon for a free sundae to the 2% of all groups of 14 people who spend the most money. At least how much must a group of 14 spend in total to get the free sundae? $_____________

5.-The average score for games played in the NFL is 21.9 and the standard deviation is 9.1 points. 8 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution ofx?x ~ N(________,_________)

b. What is the distribution ofx?x~ N(___________,__________)

c. P(x < 22.1741) =________________

d. Find the 62th percentile for the mean score for this sample size.________________

e. P(21.2741

f. Q3 for the x distribution=________________

g. P(x< 154.9928) =_______________

h. For part c) and e), is the assumption of normal necessary?Yes or No_____________