ISAT - International Student Admissions Probability and Statistical Analysis 2

Question 1

Bag: 5 red, 3 blue, 2 green. Two drawn without replacement. Probability both are red?

Accepted Answer

2/9

Answer

P = (5/10)(4/9) = 20/90 = 2/9.

Question 2

500 students, heights normally distributed: mean=170cm, SD=8cm. How many are taller than 186cm?

Accepted Answer

About 12-13

Answer

186 = mean + 2SD. About 2.5% above +2SD. 0.025 x 500 = 12.5.

Question 3

Probability of drawing a King OR a Heart from a standard 52-card deck?

Accepted Answer

4/13

Answer

P = 4/52 + 13/52 - 1/52 = 16/52 = 4/13.

Question 4

A test: 95% sensitivity, 90% specificity. Disease prevalence: 1%. What is the probability a positive result is a true positive?

Accepted Answer

Approximately 8.8%

Answer

Bayes: (0.95 x 0.01) / (0.95 x 0.01 + 0.10 x 0.99) = 0.0095/0.1085 = 8.8%.

Question 5

Dataset: 12, 15, 18, 18, 20, 22, 25, 28, 30, 35. Calculate the interquartile range.

Accepted Answer

10

Answer

Q1 = median of lower half = 18. Q3 = median of upper half = 28. IQR = 28 - 18 = 10.

ISAT - International Student Admissions Test Practice Test