Download Drawing Conclusions From Data

Avon High School
Name ________________________________
ACE College Algebra II
Worksheet 12-4 Z-Scores, Confidence Intervals,
Period ______
Drawing Conclusions From Data
For Exercises 1-2, find (a) the sample proportion, (b) the margin of error, and (c) the 95% confidence
interval for the population proportion. Express your answers as a percent to the nearest tenth.
1. In a survey of 634 randomly selected high school students, 221 planned to take an Advanced Placement
class prior to graduation.
2. In a simple random sample of 500 people, 178 reported having flu-like symptoms over the past year.
For Exercises 3-4, find (a) the margin of error, (b) the 95% confidence interval for the population
mean or population proportion, and (c) interpret the confidence interval in context.
3. A consumer research group tested the battery life of 36 randomly chosen
batteries to establish the likely battery life for the population of the same type of
battery. See table to the right.
4. In a poll of 720 likely voters, 358 indicated they plan to vote for Candidate A.
5. Roll a 6-sided die 30 times. (You can simulate this on the TI-Nspire by entering the
command “randInt(1,6,30)” on a calculator page.) In parts a) and b), find the (i) sample
proportion, (ii) the margin of error for a 95% confidence level, and (iii) the 95% confidence
interval for the population proportion.
a. rolling a 2
b. rolling a 3
c. Is the 95% confidence interval for the population proportion about the same for rolling a 2 and for rolling
a 3?
d. Compare your sample proportions to the theoretical proportions for parts (a) and (b). Would you expect
the theoretical proportion to be within the confidence intervals you found? Explain.
7. The average IQ of a group of people is 105 with a standard deviation of 15. What is the z-score of
a. someone with an IQ of 93?
b. someone with an IQ of 135?
8. Suppose a tree farm finds that the mean height of three-year-old trees is 47 inches with a standard deviation
of 3 inches.
a. Compute the z-score of a tree 51 inches tall.
b. Compute the z-score of a tree 49 inches tall.
c. A tree has a z-score of -3. How tall is it?
10. On the standard IQ test, the mean is 100 and the standard deviation is 15.
a. Compute the z-score of a person with an IQ of 120.
b. Compute the z-score of a person with an IQ of 20.
c. A person has a z-score of +3, what is her IQ?
9. A group of people is tested to see how much weight they can lift. The meanlift is 120 pouunds with a
standard deviation of 20 pounds. Compute the z-score for someone who lifts
a. 125 ponds
b. 80 pounds
c. If someone had a z-score of +3, how much can that person lift?
10. In the not too distant past, a professor at some prestigious school suggested that in an effort to combat
grade inflation, the school should issue standardized grades (or z-scores) in addition to the regular grades.
Let us see how this might work. Suppose Sue was in three classes, each with 20 students. In Intoductory
Alchemy, theprofessor awarded an A to 15 students and an A- to 5 students. The average grade point
inthis class was 3.90 and the standard deviation was 0.15. In hwe Intermediate Astrology class, the
professor was a little tougher, giving 5 A’s, five A-’s, five B+‘s, and five B’s. The GPA of the class was
3.50 with a standard deviation of 0.38. In her class of Ancient Phoenician Literature, the prof gave mostly
B’s, with a smattering of other grades, for a GPA of 2.72 and a standard deviation of 0.7.
Sue got an A- (3.67) in Alchemy, a B+ (3.33) in Astrology, and a B (3.00) in Phoenician Lit. Compute her
standardized grade in each class. If we judge by standardized grades, where did she do best? Where did
she do worst? Explain carefully.
11. A quiz in Economics has an average grade of 12 with a standard deviation of 3. The high score on the quiz
was 20. How many standard deviations above the mean was this student?
12. A group of students has an average height of 6 feet with a standard deviation of 0.25 feet.
a. Suppose we had measured in inches instead. Can we tell what their mean and standard deviation would
be? If we can tell, what would they be?
b. A student is 6.4 feet tall. How many standard deviations from the mean is he?
c. How tall is a student who is 2 standard deviations above the average?