ISAT - International Student Admissions Test International Student Admissions Probability and Statistical Analysis 1 — Questions and Answers
Question 1: From a pool of 10 international applicants (6 from Asia, 4 from Europe), 3 are randomly selected for scholarships without replacement. What is the probability that all 3 selected are from Asia?
- 1/6 (Correct answer)
- 1/5
- 1/4
- 1/3
Correct answer: 1/6
The number of ways to choose 3 from 6 Asian applicants is C(6,3) = 20. The total ways to choose 3 from 10 is C(10,3) = 120. Probability = 20/120 = 1/6 ≈ 0.167.
Question 2: IELTS scores at a university are normally distributed with a mean of 6.5 and a standard deviation of 0.5. Approximately what percentage of students score above 7.5?
- 2.5% (Correct answer)
- 5.0%
- 16.0%
- 34.0%
Correct answer: 2.5%
A score of 7.5 is exactly 2 standard deviations above the mean (z = (7.5 − 6.5) / 0.5 = 2.0). By the empirical rule, approximately 95% of data falls within ±2 SD, leaving ~5% in both tails combined, so roughly 2.5% score above 7.5.
Question 3: Of 400 applicants, 60% submitted TOEFL scores, 45% submitted IELTS scores, and 20% submitted both. What percentage of applicants submitted neither score?
- 15% (Correct answer)
- 20%
- 25%
- 35%
Correct answer: 15%
By inclusion-exclusion, P(TOEFL or IELTS) = 60% + 45% − 20% = 85%. Therefore the percentage who submitted neither = 100% − 85% = 15%.
Question 4: A student randomly guesses on every question of a 5-question multiple-choice exam, where each question has 4 options. What is the probability of getting exactly 2 questions correct?
- 0.264 (Correct answer)
- 0.125
- 0.316
- 0.500
Correct answer: 0.264
This is a binomial problem: P(X=2) = C(5,2) × (0.25)² × (0.75)³ = 10 × 0.0625 × 0.421875 ≈ 0.264.
Question 5: Eight students' test scores are: 55, 60, 70, 75, 80, 85, 90, 95. What is the interquartile range (IQR)?
- 22.5 (Correct answer)
- 25.0
- 30.0
- 35.0
Correct answer: 22.5
With 8 ordered values, Q1 is the average of the 2nd and 3rd values: (60+70)/2 = 65. Q3 is the average of the 6th and 7th values: (85+90)/2 = 87.5. IQR = 87.5 − 65 = 22.5.
Question 6: Two independent admissions screening tests each have a 70% individual pass rate. What is the probability that a student passes at least one of the two tests?
- 0.91 (Correct answer)
- 0.70
- 0.49
- 0.84
Correct answer: 0.91
P(fail both) = 0.30 × 0.30 = 0.09. P(pass at least one) = 1 − 0.09 = 0.91. Using the complement is simpler than adding individual cases.
ISAT - International Student Admissions Test International Student Admissions Probability and Statistical Analysis 1
From a pool of 10 international applicants (6 from Asia, 4 from Europe), 3 are randomly selected for scholarships without replacement.
What is the probability that all 3 selected are from Asia?