Which of the following states that the proportion of occurrences with a particular outcome converges to the probability of that outcome?
Your Answer
Score
Explanation
Law of large numbers
Correct
1.00
Law of averages
General addition rule
Bayes’ theorem
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective: Explain why the long-run relative frequency of repeated independent events settles down to the true probability as the number of trials increases, i.e. why the law of large numbers holds.
Question 2
Shown below are four Venn diagrams. In which of the diagrams does the shaded area represent A and B but not C?
Your Answer
Score
Explanation
Correct
1.00
We need the area common to events A and B to be entirely shaded except for that portion common to event C: “A and B but not C”.
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective: Draw Venn diagrams representing events and their probabilities.
Question 3
Each choice below shows a suggested probability distribution for the method of access to online course materials (desktop computer, laptop computer, tablet, smartphone). Determine which is a proper probability distribution.
Your Answer
Score
Explanation
desktop computer: 0.15, laptop computer: 0.50, tablet: 0.30, smartphone: 0.20
desktop computer: 0.25, laptop computer: 0.35, tablet: 0.15, smartphone: 0.25
Correct
1.00
Sum of all probabilities must equal 1 and each probability must be a value between 0 and 1.
desktop computer: 0.20, laptop computer: 0.20, tablet: 0.20, smartphone: 0.20
desktop computer: 0.30, laptop computer: 0.40, tablet: 0.35, smartphone: -0.05tablet2
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective: Define a probability distribution as a list of the possible outcomes with corresponding probabilities that satisfies three rules:
- The outcomes listed must be disjoint.
- Each probability must be between 0 and 1.
- The probabilities must total 1.
Question 4
Last semester, out of 170 students taking a particular statistics class, 71 students were “majoring” in social sciences and 53 students were majoring in pre-medical studies. There were 6 students who were majoring in both pre-medical studies and social sciences. What is the probability that a randomly chosen student is majoring in pre-medical studies, given that s/he is majoring in social sciences?
Your Answer
Score
Explanation
6/53
6/170
6/71
Correct
1.00
If M is the event a student is majoring in pre-medical studies and S is the event s/he is majoring in social sciences, then calculate P(M|S)=P(M&S)P(S)=671.
(71+53−6)/170
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective: Distinguish marginal and conditional probabilities.
Question 5
Which of the following is false?
Your Answer
Score
Explanation
If two outcomes of a random process (both with probability greater than 0) are mutually exclusive, they are not necessarily complements.
If two events (both with probability greater than 0) are mutually exclusive, they could be independent.
Correct
1.00
Mutually exclusive events may be complements (e.g. if a coin is flipped the probability of a Head and a Tail are both 0.5, adding up to 1) but they also might not be if there are more than two possible outcomes of the random process (e.g. a voter might be Democrat, Republican, or Independent, since being Democrat and Republican are mutually exclusive but not complements). However mutually exclusive events cannot be independent; the events are always dependent since if one event occurs we know the other one cannot.
If the probabilities of two mutually exclusive outcomes of a random process add up to 1, they are complements.
When computing the probability that a card drawn randomly from a standard deck is either a Jack or a 4, you can use the addition rule.
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective:
• Define disjoint (mutually exclusive) events as events that cannot both happen at the same time: If A and B are disjoint, P(A and B) = 0.
• Distinguish between disjoint and independent events.
- If A and B are independent, then having information on A does not tell us
anything about B (and vice versa).
- If A and B are disjoint, then knowing that A occurs tells us that B cannot occur (and vice versa).
- Disjoint (mutually exclusive) events are always dependent since if one event occurs we know the other one cannot.
Question 6
Heights of 10 year-olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Which of the following is true?
Your Answer
Score
Explanation
A normal probability plot of heights of a random sample of 500 10 year- olds people should show a fairly straight line.
Correct
1.00
Since the distribution of heights of 10 year-olds closely follow a normal distribution we would expect the normal probability plot of heights of a large sample of such kids to show a straight line.
Roughly 95% of 10 year-olds are between 37 and 73 inches tall.
We would expect more 10 year-olds to be shorter than 55 inches than taller.
A 10 year-old who is 65 inches tall would be considered more unusual than a 10 year-old who is 45 inches tall.
Total
1.00 / 1.00
Question ExplanationThis question refers to the following learning objective: Use the Z score

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