Prob/Stats: Unit 3, HW 1
Name: ____________________
Quartiles, Percentiles, and Z-Scores
1. The math test scores for a class were:
50, 65, 70, 72, 72, 78, 80, 82, 84, 84, 85, 86, 88, 88, 90, 94, 96, 98, 98, 99
Q1 = ________
Q2 = ________
Q3 = ________
𝑃33 = ________
𝑃50 = ________
Midquartile = ________
𝑃15 = ________
𝑃90 = ________
Within this context, what is the the meaning of being in the 90th percentile?
2. Twenty four history test scores for a class were:
43, 69, 98, 85, 99, 89, 72, 54, 99, 56, 79, 61, 96, 95, 62, 66, 68, 69, 70, 88, 93, 77, 87, 71
Q1 = ________
Q2 = ________
Q3 = ________
Midquartile = ________
𝑃12 = ________
𝑃20 = ________
𝑃60 = ________
𝑃5 = ________
Within this context, what is the meaning of being in the 60th percentile?
3. A particular leg bone for dinosaur fossils has a mean length of 10 feet with standard
deviation of 3 inches. What is the z-score that corresponds to a length of 62 inches?
4. An exam produced grades with a mean score of 74.2 and a standard deviation of 11.5. Find
the z-score for each test score.
a. x = 45
b. x = 81
c. x = 75.9
5. The SAT test has a mean of 500 and a standard deviation of 100. If your standard score on
this test was 1.9, what was your test score?
6. A sample has a mean of 120 and a standard deviation of 20. Find the value of x that
corresponds to each of these standard scores.
a. z = 0
b. z = 1.2
c. z = -1.4
7. What does it mean to stay that x = 152 has a standard score of +1.5?
8. What does it mean to say that a particular value of x has a z-score of -2.1?
9. In general, the z-score is a measure of what?
10. Which x value has the higher position relative to the set of data from which it comes?
A: x = 85, 𝑥̅ = 72, s = 8
B: x = 93, 𝑥̅ = 87, s = 8