1.5) Central Limit Theorem for Sums Suppose random samples of n=43n=43 are collected from an unknown distribution with the properties =42=42 and =4=4.

1. Determine the mean of X. _____________
2. Determine the standard deviation of X. ___________(Include four decimal places.)

1.6) The lengths of adult males' hands are normally distributed with mean 193 mm and standard deviation is 7.1 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.

1. What is the distribution of x? x ~ N(______,________)
2. For the group of 45, find the probability that the average hand length is more than 192. ____________
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? No or Yes

1.7) The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 6 ounces. 32 randomly selected people are surveyed. 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 drinks between 15.9 and 16.1 ounces of coffee per day? _____________
4. For the 32 people, find the probability that the average coffee consumption is between 15.9 and 16.1 ounces of coffee per day. ___________
5. For part d), is the assumption that the distribution is normal necessary? No or Yes
6. Find the IQR for the average of 32 coffee drinkers. Q1 = _____________ ounces Q3 = _____________ ounces IQR: ______________ ounces

1.8) The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.4 minutes. 47 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(________,_________)
2. What is the distribution of x? x ~ N(_______,________)
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 24.6748 and 25.1748 minutes. ______________
5. For the 47 runners, find the probability that their average time is between 24.6748 and 25.1748 minutes. ______________
6. Find the probability that the randomly selected 47 person team will have a total time more than 1165.6. _______
7. For part e) and f), is the assumption of normal necessary? Yes or No
8. The top 15% of all 47 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? ______________ minutes