Suppose there are twelve multiple choice questions in an English class quiz. Each question has five possible answers, and only one of them is correct. Find the probability of having four or less correct answers if a student attempts to answer every question at random.
pbinom(4, size=12, prob=1/5)## [1] 0.9274445If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particular minute.
ppois(16, lambda=12, lower.tail=F)## [1] 0.101291Suppose the mean checkout time of a supermarket cashier is three minutes. Find the probability of a customer checkout being completed by the cashier in less than two minutes.
pexp(2, rate=1/3)## [1] 0.4865829Assume that the test scores of a college entrance exam fits a normal distribution. Furthermore, the mean test score is 72, and the standard deviation is 15.2. What is the percentage of students scoring 84 or more in the exam?
pnorm(84, mean=72, sd=15.2, lower.tail=F)## [1] 0.2149176Find the 2.5th and 97.5th percentiles of the Student t distribution with 5 degrees of freedom.
qt(c(0.025, 0.975), df=5)## [1] -2.570582 2.570582