ISAT Probability and Statistical Analysis 5

Question 1

In a sample of 200 students, 80 play sports. What is the relative frequency of students who play sports?

Accepted Answer

40%

Answer

Relative frequency = 80/200 = 0.40 = 40%.

Question 2

A probability distribution has E(X) = 5 and Var(X) = 4. What is the standard deviation of X?

Accepted Answer

2

Answer

Standard deviation = √Var(X) = √4 = 2.

Question 3

Bayes' theorem is used to:

Accepted Answer

Update probability based on new evidence

Answer

Bayes' theorem revises the probability of a hypothesis as additional evidence is incorporated.

Question 4

A data set: 3, 7, 7, 9, 11. What is the mode?

Accepted Answer

7

Answer

The mode is 7 because it appears twice, more than any other value in the dataset.

Question 5

If P(A) = 0.4 and P(A|B) = 0.4, what can be concluded about events A and B?

Accepted Answer

A and B are independent

Answer

Since P(A|B) = P(A), knowing B occurred doesn't change the probability of A, so A and B are independent.

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