4. Probability

In a survey of all students at a university, it was found that the average GPA is $3.2$. Is the underlined number $3.2$ a statistic or a parameter?

Suppose events E and F are such that $P(E\cap F)$ = $P\left(E\right)$ $\times$ $P\left(F\right)$. Are the events E and F independent or dependent? Justify your answer.

If you flip a fair coin, what is the probability of getting heads? Express your answer as a percentage.

Which of the following best describes the difference between $\mathrm{univariate}$ data and $\mathrm{bivariate}$ data?

If an event has a probability of $\frac{3}{4}$, how likely is it to occur?

Which of the following is not a voluntary response sample?

A bag contains $12$ marbles numbered $1$ to $12$. If a marble is chosen at random, what is the probability that it is either shaded (suppose marbles numbered $2$, $4$, $6$, $8$, $10$, and $12$ are shaded) or is labeled with a multiple of $3$?

Suppose you are given the following data for two variables, $X$ and $Y$: $(1,2)$, $(2,4)$, $(3,6)$, $(4,8)$. What is the value of the sample correlation coefficient between $X$ and $Y$? Do not round your intermediate calculations.

Suppose a researcher wants to determine the average height of all students currently enrolled at a large university. Should the researcher collect data from a sample or from the entire population?

Given any two events $A$ and $B$, which of the following correctly expresses the probability of their union $P(A\cup B)$?

Given a table that lists the number of cars sold by a dealership each day, is the random variable representing the number of cars sold discrete or continuous?

Which of the following best describes the difference between a $\mathrm{census}$ and a $\mathrm{sampling}$ in statistics?

Suppose a standard deck contains cards that are either striped or solid, and either blue or red. If the probability that a card is striped is $\frac{1}{2}$ and the probability that a card is blue is $\frac{1}{4}$, and being striped and being blue are independent events, what is the probability that a randomly selected card is both striped and blue?

A racehorse wins $5$ of its first $7$ races. What is the ratio of the number of races won to the number of races lost?

Which two essential features are present in all statistically designed experiments?