4. Probability

Which of the following statements correctly verifies that the function $p\left(x\right)=\frac{1}{4}$ for $x=1$, $x=2$, $x=3$, $x=4$ and $p\left(x\right)=0$ otherwise is a probability mass function?

Which of the following is a probabilistic system?

In which type of statistical study is the population influenced by researchers?

In a survey, $10$ out of every $32$ people play Among Us. What percent of the people surveyed play Among Us?

Suppose a normal distribution has mean $\mu$ and standard deviation $\sigma$. According to the empirical rule, what is the approximate probability that a randomly selected value from this distribution falls within one standard deviation of the mean (that is, between $\mu -\sigma$ and $\mu +\sigma$)?

If you toss a fair coin $20$ times, what is the probability that it lands on tails in a single toss?

In the context of basic concepts of probability, how do scientists use $probability$ when describing risks?

Suppose the error involved in making a certain measurement is a continuous random variable $x$ with cumulative distribution function (cdf) $F\left(x\right)=\{\begin{array}{cc}0& ,x<0\\ \frac{x}{2}& ,0\le x<2\\ 1& ,x\ge 2\end{array}$. What is the probability that the error is less than 1.5?

In the context of quality control, which probability distribution is most commonly used to calculate the probability of producing a defect in a single trial?

In the context of probability and statistics, which of the following best describes what it means for two variables to be positively associated and negatively associated?

Which of the following research questions would not be tested using inferential statistics?

Which of the following expressions represent the same probability value as $\frac{1}{4}$?

If $18$ out of $30$ students in a class passed an exam, what is the probability that a randomly selected student from this class passed the exam? Express your answer as a simplified fraction.

Which of the following correctly represents the formula for the probability of the union of two events $A$ and $B$ in probability theory?

Given that $X$ has a Poisson distribution with parameter $\lambda$, which of the following is the correct expression for the probability that $X$ equals $k$?