The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of 5 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 13.7 and 14.3 ounces of coffee per day?___________
4. For the 32 people, find the probability that the average coffee consumption is between 13.7 and 14.3 ounces of coffee per day. _____________
5. Find the IQR for the average of 32 coffee drinkers. Q1 = ____________ ounces Q3 =____________ ounces IQR: ____________ ounces

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.6 ppm. 11 randomly selected large cities are studied. 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 city's waterway will have more than 10.3 ppm pollutants? _________________
4. For the 11 cities, find the probability that the average amount of pollutants is more than 10.3 ppm. _______________
5. Find the IQR for the average of 11 cities. Q1 = ___________ ppm Q3 = ___________ ppm IQR: ____________ ppm

The lengths of adult males' hands are normally distributed with mean 191 mm and standard deviation is 7.4 mm. Suppose that 49 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 49, 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? ______________

Central Limit Theorem for Sums Suppose random samples of n=49 are collected from an unknown distribution with the properties =47 and =4.

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

Application of The Central Limit Theorem for Sums 100 North Main Street is the tallest building in Winston-Salem, NC standing at 460ft tall (5520inches). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator)

1. Given that the heights of American women follow the distribution N(65,3.5), what is the probability of that a random sample of 85 women, stacked head-to-foot, would be at least as tall as 100 North Main Street?
   1. P(X5520)= ______________ (Include three decimal places.)
   2. Determine the z-score of X=5520 for a sample of 85. z=_____________ (Include three decimal places.)

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 19 minutes. A researcher observed 14 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(________,________)
2. What is the distribution of x? x ~ N(________,__________)
3. What is the distribution of x? x~ N(_________,________)
4. If one randomly selected student is timed, find the probability that this student's time will be between 37 and 42 minutes. ________________
5. For the 14 students, find the probability that their average time studying is between 37 and 42 minutes. ____________
6. Find the probability that the randomly selected 14 students will have a total study time less than 546 minutes. ____________
7. For part e) and f), is the assumption of normal necessary? ___ yes or ___no
8. The top 20% of the total study time for groups of 14 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