Please only choose what kind of distribution is best to be used from the multipl

Question

Please only choose what kind of distribution is best to be used from the multiple choices. Do not work out the problems.

In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. How many people are expected to be tested before 2 with the gene are detected? a. Binomial b. Negative Binomial c. Hypergeometric d. Poisson e. Normal f. Exponential g. Lognormal A second-stage smog alert has been called in a certain area in Los Angeles County in which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations. If 15 of the firms are actually violating at least one regulation, what is the probability that none of the ten of the visited firms will have a violation? a. Binomial b. Negative Binomial c. Hypergeometric d. Poisson e. Normal f. Exponential g. Lognormal Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. What is the probability that every passenger who shows up can take the flight? a. Binomial b. Negative Binomial c. Hypergeometric d. Poisson e. Normal f. Exponential g. Lognormal

Explanation / Answer

a)

Here , x be the number of people are expected to be tested befor 2 with the gen detected.

Distribution of x is Negative Binomial distribution.

It is generalization of geometric distribution in which ranodm variable is the number of bernoulli trials required to obtain r success.

b)

Here x be the number of firms that have violations in 10 firms selected from 50 in which 15 firms have violations.

Distribution of x is Hypergeometric.

In Hypergeometric distribution random variable is number of successes x drawn from r available in n selection.

c )

Here x be the number of passengers shown up.

x follows Binomial distribution with parameter p = 0.9 and n = 125

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