3.

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 49 minutes and standard deviation 16 minutes. A researcher observed 42 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. What is the distribution of xx? xx ~ N(,)
4. If one randomly selected student is timed, find the probability that this student's time will be between 48 and 51 minutes.
5. For the 42 students, find the probability that their average time studying is between 48 and 51 minutes.
6. Find the probability that the randomly selected 42 students will have a total study time less than 2226 minutes.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 15% of the total study time for groups of 42 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

5.

Central Limit Theorem for Sums

Suppose random samples of n=45n=45 are collected from an unknown distribution with the properties =54=54 and =3=3.

1. Determine the mean of XX.

1. Determine the standard deviation of XX. (Include four decimal places.)

6.

The lengths of adult males' hands are normally distributed with mean 186 mm and standard deviation is 7.2 mm. Suppose that 41 individuals are randomly chosen. Round all answers to 4 where possible.

1. What is the distribution of xx? xx ~ N(,)
2. For the group of 41, find the probability that the average hand length is more than 184.
3. Find the third 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? NoYes

7.

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.8 ppm and standard deviation 1.4 ppm. 18 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. What is the probability that one randomly selected city's waterway will have less than 8.8 ppm pollutants?
4. For the 18 cities, find the probability that the average amount of pollutants is less than 8.8 ppm.
5. For part d), is the assumption that the distribution is normal necessary? YesNo
6. Find the IQR for the average of 18 cities.
7. Q1 = ppm
8. Q3 = ppm
9. IQR: ppm

8.

The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.7 minutes. 13 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 XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. What is the distribution of xx? xx ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 22.8768 and 23.7768 minutes.
5. For the 13 runners, find the probability that their average time is between 22.8768 and 23.7768 minutes.
6. Find the probability that the randomly selected 13 person team will have a total time less than 289.9.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 10% of all 13 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