Identify each of the following statements as either TRUE or FALSE

1.Identify each of the following statements as either TRUE or FALSE.a) (Click for List) False True In a hypergeometric distribution, if M is the number of successes in the population, and N is the population size, then there are N+M failures in the population.b) (Click for List) False True In a hypergeometric distribution, the random variable X must be greater than or equal to 0.c) (Click for List) False True In a hypergeometric distribution, if x is the number of successes in a sample size of n, then n – x is the number of failures in the sample.d) (Click for List) True False The hypergeometric distribution depends on the population size, the sample size, and number of successes within the population.e) (Click for List) False True The maximum value the random variable X can take on in a hypergeometric distribution is M, the number of successes in the population.2. LetXbe a discrete random variable that follows a geometric distribution withp =0.26.What is P(X = 6)?Round your answer to at least 3 decimal places.3. A dentist believes that 1 in 2 people have gingivitis. Supposing that the dentist’s belief is correct, that 1 in 2 people actually do have gingivitis, then on any given day in his office, what is the probability that the first case of gingivitis he sees will be on his second patient?(We will assume for the purposes of this question that his patients are all independent of each other).Round your answer to at least 3 decimal places.4. Identify each of the following statements as either TRUE or FALSE.a) (Click for List) True False The mean of a Poisson random variable can be negative.b) (Click for List) True False If X is a Poisson random variable, then X represents a count.c) (Click for List) True False There are no parameters in a Poisson distribution.d) (Click for List) False True The smallest value a Poisson random variable can be is 0.e) (Click for List) True False A Poisson distribution can be applied when counting the number of times an event of interest occurs over time, volume, area or distance.5. In order to qualify for a job opening, applicants must have a some experience in statistics. 50 individuals submit an application for the job, of which only 10 individuals actually have experience with statistics. Suppose that 5 applicants are randomly selected to be interviewed on the first day, with the remaining applicants to be interviewed later in the week (we can assume that once an individual has been selected to be interviewed, he or she will not be selected again). What is the probability that of the first 5 applicants to be interviewed, at least one of them will have statistical experience?Round your answer to at least 3 decimal places.6. LetXbe a discrete random variable that follows a Poisson distribution with?=6.What is P(X=3)?Round your answer to at least 3 decimal places.