AP Statistics
Chapter 2 Worksheet 1
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Period:
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You may work with 1 partner on this activity. This is an important assignment – try your best!
Directions: For the questions below, assume the populations are normally distributed, answer the questions
using standardization (z-scores), Table A from your book, and the procedure we learned on Friday.
For each question:
Show your work leading to your answer.
Draw an appropriate normal curve with the region under the curve indicated and shaded.
Example: Bobby wants to know his percentile on the CST math Geometry test if he receives a 378 on the test.
He finds out from his school that the mean score is 350 with a standard deviation of 50.
1. Fernando is 60 inches tall. The average height for his age and gender is 68 with a standard deviation of
10 inches. Find Fernando’s z-score and percentile. What percent of his peers are shorter than him? What
percent are taller?
2. Susan took the SAT math and scored a 652. The mean score on the SAT math is 580 with a standard
deviation of 100. Find Susan’s z-score and percentile. What percent of students scored lower than Susan
on the SAT math? What percent scored higher?
3. Tabitha is studying concentrations of a fertilizer in local rivers and lakes. The average level of fertilizer is
50 ppm with a standard deviation of 6 ppm. She tests a sample from the delta and finds it to contain 60
ppm of fertilizer. What percent of rivers and lakes have a higher level?
4. The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent
of students in the course have a GPA between 2.9 and 3.8? Confirm your answer against the 68-95-99.7
rule.
5. The average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years.
What percent of fans are between 18 and 27 years old?
6. The number of eggs produced by a type of sea turtle has a mean of 102.7 and a standard deviation of
26.8. What percent of turtles lay between 100 and 150 eggs?
7. Challenge Question: The average score on the Chapter 1 Geometry test was 75 with a standard
deviation of 10. If your teacher tells you that you were in the 70th percentile, what was your score on the
test?
Hint: Look at the z-table and find the P value (middle of table) that is .7000 or closest to that value. Find out
which z-value that corresponds to by looking over/up. Once you know that z-score, work backwards using
this formula:
z
x
