ISAT - International Student Admissions Probability and Statistical Analysis Questions and Answers

Question 1

A research group is studying the weekly screen time of teenagers.
They collect the following data in hours from a sample of 7 participants: 15, 18, 20, 22, 25, 28, 75.
Which measure of central tendency would most accurately describe a typical teenager's screen time in this sample?

Accepted Answer

The median, because it is not significantly affected by the outlier.

Answer

The mean, because it includes all data points.

Answer

The mode, because it represents the most frequent value.

Answer

The range, because it shows the full spread of the data.

Question 2

A city's health department observes that during summer months, sales of ice cream are strongly and positively correlated with the number of heatstroke incidents. They conclude that consuming ice cream causes heatstroke. Which of the following statements best describes the flaw in their conclusion?

Accepted Answer

A third variable, high temperatures, is likely the cause of both increased ice cream sales and more heatstroke incidents.

Answer

The conclusion is valid as the statistical correlation is strong.

Answer

The sample size was likely too small to draw a valid conclusion.

Answer

The direction of causality is reversed; heatstroke causes people to eat ice cream.

Question 3

A quality control inspector is examining two production lines, Line A and Line B, which both produce bolts with a target length of 50 mm. The inspector takes a sample from each line. Line A's sample has lengths (in mm) of {49, 51, 50, 49, 51}. Line B's sample has lengths of {45, 55, 50, 47, 53}. Both samples have a mean of 50 mm. Which of the following statements is true regarding the samples?

Accepted Answer

Line B has a larger standard deviation than Line A.

Answer

Line A has a larger standard deviation than Line B.

Answer

Both lines have the same standard deviation.

Answer

The standard deviation cannot be determined without more data.

Question 4

An office has 100 employees. 60% of the employees are women. 30% of all employees have advanced degrees. Of the employees with advanced degrees, 20 are women. What is the probability that a randomly selected employee is a man who does not have an advanced degree?

Accepted Answer

0.30

Answer

0.20

Answer

0.40

Answer

0.10

Question 5

In a class of 50 students, 30 students are enrolled in Chemistry and 25 students are enrolled in Physics. 10 students are enrolled in both subjects. What is the probability that a randomly selected student is enrolled in Chemistry, given that they are enrolled in Physics?

Accepted Answer

2/5

Answer

1/3

Answer

1/5

Answer

3/5

Question 6

A box contains 6 red balls, 4 blue balls, and 5 green balls. If two balls are drawn from the box one after the other without replacement, what is the probability that both balls are red?

Accepted Answer

1/7

Answer

1/5

Answer

4/25

Answer

1/9

A research group is studying the weekly screen time of teenagers.They collect the following data in hours from a sample of 7 participants: 15, 18, 20, 22, 25, 28, 75.Which measure of central tendency would most accurately describe a typical teenager's screen time in this sample?

A research group is studying the weekly screen time of teenagers.
They collect the following data in hours from a sample of 7 participants: 15, 18, 20, 22, 25, 28, 75.
Which measure of central tendency would most accurately describe a typical teenager's screen time in this sample?