Statistics and Probability practice questions.

For a continuous random variable X with pdf f, what is P(X = a) for any single value a?

• f(a)
• 0
• 1
• undefined

Answer: 0

Probabilities for continuous variables are areas under the pdf; a single point has zero width, so P(X = a) = 0. Consequently P(X ≤ a) = P(X < a).

Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.4. Find P(A ∪ B).

• 0.12
• 0.58
• 0.7
• 1

Answer: 0.7

Mutually exclusive means P(A ∩ B) = 0, so P(A ∪ B) = 0.3 + 0.4 = 0.7. (0.58 would be the answer if A and B were independent instead.)

In a normal distribution, approximately what percentage of values lie within one standard deviation of the mean?

• 50%
• 68%
• 95%
• 99.7%

Answer: 68%

The empirical rule: about 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.

A college has 300 first-year and 200 second-year students. A stratified sample of 50 students is taken, proportional to year group. Determine how many first-year students are in the sample.

• 20
• 25
• 30
• 35

Answer: 30

First-years make up 300/500 = 3/5 of the population, so the sample contains 3/5 × 50 = 30 first-year students.

A supermarket manager selects every 12th customer entering the store, starting from a randomly chosen customer among the first 12. State the sampling technique being used.

• Systematic sampling
• Stratified sampling
• Quota sampling
• Simple random sampling

Answer: Systematic sampling

Selecting members at a fixed interval from a random starting point is systematic sampling.

Which of the following variables is discrete?

• The height of a sunflower
• The time taken to swim 50 m
• The mass of a parcel
• The number of daily emails

Answer: The number of daily emails

A count of emails can only take whole-number values, so it is discrete; height, time and mass are measured on a continuous scale.