Question

A small class has 10 students. Seven of the students are male and 3 are female. You write the name of each student on a small card. The cards are shuffled thoroughly and you choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled and you again choose a card at random, observe the name, and replace it in the set. This is done a total of five times. Let X be the number of cards observed in these four trials with a name corresponding to a male student. The random variable X has which of the following probability distributions? the Normal distribution, with mean 3 and variance 1 the binomial distribution, with parameters n = 5 and p = 0.3 * the binomial distribution, with parameters n = 5 and p = 0.7

Answer 1

Answer:

last one. B(5,0.7)

Step-by-step explanation:

Since no. of times getting a Male is discrete and probability of success is constant, it will follow a binomial distribution.

Let X be the no. of males

Then X ~ B(5, 0.7)

Where 5 is the no. of trials and 0.7 is the probability of success

Success is getting a Male.

So probability of success = 7/10 =0.7

Answer 2

Answer:

The binomial distribution, with parameters n = 5 and p = 0.7

Step-by-step explanation:

For each card observed, there are only two possible outcomes. Either it is a name corresponding to a male student, or it is a name corresponding to a female student. Since the cards are replaced, that is, place back in the set, the propability of taking a male student is each obervation is independent from other observations. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

This is done a total of five times.

Which means that $n = 5$

Let X be the number of cards observed in these five trials with a name corresponding to a male student.

Each trial, there is a 7/10 probability of observing a male student. So

$p = \frac{7}{10} = 0.7$

So the correct answer is:

The binomial distribution, with parameters n = 5 and p = 0.7