1) A statistics exam has 50 multiple choice questions. For each of these questions, a choice of 5 answers is suggested, only one of which is correct. A correct answer is worth 2 points while a wrong answer is worth 0 points. Consider the case of a student who did not study for the exam at all and decides to answer all 50 questions at random. Let X be the numerical mark obtained by this student. What is the variance of X?

2) According to data collected over several years, the number of patients who enter the emergency department of a hospital in the Laurentian region each hour follows a Poisson distribution of mean = 12. What is the probability that in 45 minutes the number of patients entering this department will equal 7?

3) In an online sales company, historically, it has been observed that 5% of orders are canceled before they are processed. Consider a day when we received 24 online orders. Suppose the orders are independent, what is the probability that at least 22 of these orders will not be canceled before they are processed?

4) If X is a random variable that follows a binomial distribution B (n; p = 0.4), the value of n being unknown. Knowing that the expectation E [X]

is equal to 16, find the value of n.

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