Discrete vs Continuous Distributions

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Show your work for each problem.

1.
Which variable is discrete?
1. a)Number of students in a class
2. b)Height of a tree
3. c)Temperature of water
4. d)Distance traveled
2.
Which variable is continuous?
1. a)Number of cars in a parking lot
2. b)Number of emails received
3. c)Number of goals scored
4. d)Weight of a newborn baby
3.
A fair die is rolled. What is ? Give your answer as a fraction.
4.
Is 'number of pages in a book' discrete or continuous? Answer with one word.
5.
For a continuous distribution, what is ?
1. a)Cannot be determined
2. b)1
3. c)0.5
4. d)0
6.
Classify each variable: (a) Time to run a marathon, (b) Number of children in a family, (c) Blood pressure reading
7.
A fair die is rolled. What is ? Give your answer as a fraction.
8.
Why do we use PMF for discrete distributions and PDF for continuous distributions?
1. a)PMF is for large numbers; PDF is for small numbers
2. b)PMF uses decimals; PDF uses fractions
3. c)They are interchangeable terms
4. d)PMF gives exact probabilities; PDF gives density that must be integrated
9.
A coin is flipped 3 times. Find where X is the number of heads.
10.
Is 'exact time you wake up' (to the millisecond) discrete or continuous?
11.
Heights follow a normal (continuous) distribution. Explain why , yet people with height 175 cm exist.
12.
A variable can take values 0, 0.5, 1, 1.5, 2, 2.5, ... Is it discrete or continuous?
1. a)Continuous - the values include decimals
2. b)Discrete - the values are listable and separate
3. c)Neither - it's a mixed distribution
4. d)Cannot be determined
13.
A spinner has 5 equal sections numbered 1-5. Find the probability of getting an even number.
14.
For a fair die, what is ? Give your answer as a fraction.
15.
Is 'amount of rainfall in a month' discrete or continuous? Then, is 'number of rainy days in a month' discrete or continuous?