ISAT - International Student Admissions Test International Student Admissions Probability and Statistical Analysis 1

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?

Accepted Answer

1/6

Answer

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?

Accepted Answer

2.5%

Answer

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?

Accepted Answer

15%

Answer

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?

Accepted Answer

0.264

Answer

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)?

Accepted Answer

22.5

Answer

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.

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Test International Student Admissions Probability and Statistical Analysis 1