STAT130 SI SESSION 10 QUIZ

True or False: The t-distribution becomes identical to the z-distribution when degrees of freedom → ∞.

• True
• False

Which of the following is NOT a characteristic of the binomial distribution?

• a) Fixed number of trials

• b) Trials are independent

• c) Constant probability of success

• d) Outcomes must be numeric

If A and B are independent, which must be true?

• a) P(A ∪ B) = 1

• b) P(A ∩ B) = P(A) + P(B)

• c) P(A|B) = P(A)

• d) P(A ∩ B) = 0

A call center receives 3 calls/hour on average. What's the probability of exactly 2 calls in the next hour?

• a) 0.2240

• b) 0.1494

• c) 0.4232

• d) 0.1804

What does the standardization formula Z = (X - μ)/σ help with?

• a) Changing units

• b) Comparing across different scales

• c) Converting to normal distribution

• d) All of the above

A key characteristic of the chi-square distribution is that it:

• a) Is symmetric

• b) Can be negative

• c) Is skewed right

• d) Has a mean of zero

The law of total probability is used:

• a) When events are mutually exclusive

• b) Only in frequentist methods

• c) To find marginal probabilities using conditional ones

• d) When probabilities are unknown

A distinguishing feature of the Poisson distribution is:

• a) It has two parameters

• b) It models rare events over a fixed interval

• c) It is used for proportions

• d) It requires normality of data

True or False: A permutation is always greater than or equal to the corresponding combination.

• True
• False

A situation with a fixed number of trials and success/failure outcomes is best modeled using:

• a) Poisson

• b) Chi-square

• c) Binomial

• d) Normal