1. The random variable [latex]X[latex] is normally distributed. The values [latex]650[latex] and [latex]850[latex] are at the [latex]60[latex]th and [latex]90[latex]th percentiles of the distribution of [latex]X[latex], respectively.
| Quantity A | Quantity B |
| The value at the [latex]75[latex]th percentile of the distribution of [latex]X[latex] | [latex]750[latex] |
2. Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below.
(a) What are the range, the three quartiles, and the interquartile range of the measurements?
(b) If the [latex]80[latex]th percentile of the measurements is [latex]130[latex] milligrams, about how many measurements are between [latex]126[latex] milligrams and [latex]130[latex] milligrams?
3. The company at which Mark is employed has [latex]80[latex] employees, each of whom has a different salary. Mark’s salary of $[latex]43,700[latex] is the second-highest salary in the first quartile of the [latex]80[latex] salaries. If the company were to hire [latex]8[latex] new employees at salaries that are less than the lowest of the [latex]80[latex] salaries, what would Mark’s salary be with respect to the quartiles of the [latex]88[latex] salaries at the company, assuming no other changes in the salaries?
(A) The fourth-highest salary in the first quartile
(B) The highest salary in the first quartile
(C) The second-lowest salary in the second quartile
(D) The third-lowest salary in the second quartile
(E) The fifth-lowest salary in the second quartile
4. The median income of a group of College [latex]C[latex] graduates six months after graduation was $[latex]3,000[latex] higher than the median income of a group of College [latex]D[latex] graduates six months after graduation.
| Quantity A | Quantity B |
| The [latex]75[latex]th percentile of the incomes of the group of College [latex]C[latex] graduates six months after graduation | The [latex]75[latex]th percentile of the incomes of the group of College [latex]D[latex] graduates six months after graduation |
5. The [latex]75[latex]th percentile on a test corresponded to a score of [latex]700[latex], while the [latex]25[latex]th percentile corresponded to a score of [latex]450[latex].
| Quantity A | Quantity B |
| [latex]800[latex] | A [latex]95[latex]th percentile score |
6. Set [latex]S[latex] = {[latex]2, 5, 7, 11, 16, 24, 28, 50, 52, 101, 120, 130[latex]}
What is the average of the first quartile (“[latex]Q1[latex]”) and the third quartile (“[latex]Q3[latex]”) of set [latex]S[latex]?
(A) [latex]9[latex]
(B) [latex]26[latex]
(C) [latex]42.75[latex]
(D) [latex]76.5[latex]
(E) [latex]85.5[latex]
7. The test scores at Millbrook High School are normally distributed, and the [latex]60[latex]th percentile is equal to a score of [latex]70[latex].
| Quantity A | Quantity B |
| The 30th percentile score | [latex]35[latex] |
8. Exam grades among the students in Ms. Harshman’s class are normally distributed, and the [latex]50[latex]th percentile is equal to a score of [latex]77[latex].
| Quantity A | Quantity B |
| The number of students who scored less than [latex]80[latex] on the exam | The number of students who scored greater than [latex]74[latex] on the exam |
9. The length of bolts made in factory [latex]Z[latex] is normally distributed, with a mean length of [latex]0.1630[latex] meters and a standard deviation of [latex]0.0084[latex] meters. The probability that a randomly selected bolt is between [latex]0.1546[latex] meters and [latex]0.1756[latex] meters long is between
(A) [latex]54[latex]% and [latex]61[latex]%
(B) [latex]61[latex]% and [latex]68[latex]%
(C) [latex]68[latex]% and [latex]75[latex]%
(D) [latex]75[latex]% and [latex]82[latex]%
(E) [latex]82[latex]% and [latex]89[latex]%
10. Jane scored in the [latex]68[latex]th percentile on a test, and John scored in the [latex]32[latex]nd percentile.
| Quantity A | Quantity B |
| The proportion of the class that received a score less than John’s score | The proportion of the class that scored as high as or higher than Jane |
11. In a set of [latex]10[latex] million numbers, one percentile would represent what percent of the total number of terms?
(A) [latex]1,000,000[latex]
(B) [latex]100,000[latex]
(C) [latex]10,000[latex]
(D) [latex]100[latex]
(E) [latex]1[latex]
12. On a particular test whose scores are distributed normally, the [latex]2[latex]nd percentile is [latex]1720[latex], while the [latex]84[latex]th percentile is [latex]1990[latex]. What score, rounded to the nearest [latex]10[latex], most closely corresponds to the [latex]16[latex]th percentile?
(A) [latex]1,750[latex]
(B) [latex]1,770[latex]
(C) [latex]1,790[latex]
(D) [latex]1,810[latex]
(E) [latex]1,830[latex]
13. [latex]300[latex] test results are integers ranging from [latex]15[latex] to [latex]75[latex], inclusive. Dominick’s result is clearly in the [latex]80[latex]th percentile of those results, not the [latex]79[latex]th or the [latex]8[latex]1st.
| Quantity A | Quantity B |
| Number of other test results in the same percentile as Dominick’s | Maximum number of other test-takers with the same result as Dominick |
14. The outcome of a standardized test is an integer between [latex]151[latex] and [latex]200[latex], inclusive. The percentiles of [latex]400[latex] test scores are calculated, and the scores are divided into corresponding percentile groups.
| Quantity A | Quantity B |
| Minimum number of integers between [latex]151[latex] and [latex]200[latex], inclusive, that include more than one percentile group | Minimum number of percentile groups that correspond to a score of [latex]200[latex] |
Answer:
1 B
2 (a) range=41, Q1 =114, Q2 =118, Q3 =126, interquartilerange=12 (b) 40 measurements
3 E
4 D
5 D
6 C
7 D
8 C
9 D
10 C
11 E
12 D
13 C
14 A
