Download Geo C - Loudoun County Public Schools

AP Stats
Chap 6
Classwork
Name __________________________________________ Pd __________
Show all necessary work and place your answers on separate paper.
Weighting a quiz.
1. Suppose the class takes a 40-point quiz. Results show a mean score of 30, median 32, IQR 8, SD 6,
min 12, and Q1 27. Your personal score was a 35. Make a table showing what each of these vales
becomes if…
a. the quiz is weighted as 50 points. Meaning…every student gets 10 points, and you now have a 45.
b. the quiz is weighted as 80 points. Meaning…every score is doubled, and yours is now a 70.
c. the quiz is weighted as 100 points. Meaning…every score is doubled and then 20 points are added,
you now have a 90.
Track and Field.
2. Three competitors each compete in three events. Their
results are listed in the table, as are the mean and
standard deviation of the results of each event. Note
that each placed first, second, and third in an event.
Who gets the gold medal? Who gets the silver?
The bronze? Who turned in the most remarkable
performance of the competition?
Fuel Efficiency.
3. Suppose a Normal model describes the fuel efficiency of cars currently registered in the
Commonwealth of Virginia. The mean is reported as 24 mpg, with a standard deviation of 6 mpg.
a. Sketch the Normal model.
b. What percent of all cars get less than 15 mpg?
c. What percent of all cars get between 20 and 30 mpg?
d. What percent of cars get more than 40 mpg?
e. Describe the fuel efficiency of the worst 20% of all cars.
f. What gas mileage represents the third quartile?
g. Describe the gas mileage of the most efficient 5% of all cars.
h. What gas mileage would you consider unusual? Why?
i. An ecology group is lobbying for a national goal calling for no more than 10% of all cars to be
under 20 mpg. If the standard deviation does not change, what average fuel economy must
be attained?
j. Car manufacturers argue that they cannot raise the average as much as you just computed.
They believe that they can only get to 26 mpg. What standard deviation would allow them
to meet the “only 10% under 20 mpg” goal?
k. What change in the fuel economy of cars would achieving that standard deviation bring about?
Class Size.
4. During a budget meeting, the school board members for Loudoun County Public Schools decided to
review class size information to determine if budgets were correct. Summary statistics are shown
in the table.
a. Notice that the third quartile and maximum class sizes are the same. Explain how this can be.
b. The school district declares that classes with enrollments of fewer than 20 students are “too
small.” Would you consider a class of 20 students – in this example – to be unusually
small? Explain.
More School Board.
5. The school district sets the office supply budgets of their high school on the enrollment of students.
The district budgets each class $12 plus $0.75 per student, so a class with 40 students would
receive 12 + 0.75(40) = $42, for instance.
a. What is the median class budget for office supplies?
b. What is the IQR?
c. What is the mean?
d. What is the standard deviation?
The Post Office.
6. The Postmaster of Sterling’s Post Office believes that a Normal model is useful in projecting the
number of letters which will be mailed during the day. He uses a mean of 20,000 letters and a
standard deviation of 250 letters. Draw and clearly label this model.
Light Bulbs.
7. Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A standard
white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white
light bulb has a mean life of 700 hours and a standard deviation of 35 hours. As part of the
science fair, both light bulbs lasted 750 hours. Which light bulbs life span was better? Explain.
Getting to Work on Time.
8. At a large business, employees must report to work at 7:30 am. The arrival times of employees can be
described as Normal model with mean of 7:22 am and a standard deviation of 4 minutes.
a. What percent of employees are late on a typical work day?
b. A psychological study determined that the typical worker needs five minutes to adjust to their
surroundings before beginning their duties. What percent of this business’ employees
arrive early enough to make this adjustment?
c. Because last employees are a distraction and cost companies money, all employees need to be
on time to work. If the mean arrival time of employees does not change, what standard
deviation would the arrival times need to ensure virtually all employees are on time to
work?
d. Explain what achieving a smaller standard deviation means in the context of this question.