Which one of these variables is a continuous random variable

Which one of these variables is a continuous random variable?

a. The time it take a randomly selected student to complete an exam

b. The number of children in a family

c. The number of women taller than 68 inches in a random sample of 5     women.

d, The number of correct guesses an a multiple choice test.

2.Selection of favorite fruits and responses of orange, grape, apple, kiwi or other many were recorded are

a.Probability distribution

b.Binomial distribution

c.Poisson distribution

d.none

Please explain

Solution

Which one of these variables is a continuous random variable?

a. The time it take a randomly selected student to complete an exam [ANSWER]

A continuous variable can take any value on a certain interval. Here, the student can complete an exam in 34.32897 minutes. For the other choices, you can\'t have decimal values.

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2.Selection of favorite fruits and responses of orange, grape, apple, kiwi or other many were recorded are

a. Probability distribution. [ANSWER]

It is not a binomial because there are not only 2 outcomes. It is not Poisson because this is a categorical variable. However, we can present this as a probability distribution, giving each fruit its own probability.