Question

A poll found that 25​% of adults do not work at all while on summer vacation. In a random sample of 10 ​adults, let x represent the number who do not work during summer vacation. Complete parts a through e.

Explain why x is (approximately) a binomial random variable. Choose the correct answer below.

A. The experiment consists of only identical trials.
B. The experiment consists of identical trials, there are only two possible outcomes on each trial (wworks or does not work). and the trials are independent.
C. The trials are not independent
D. There are three possible outcomes on each trial

Answer 1

Answer:

B. The experiment consists of identical trials, there are only two possible outcomes on each trial (wworks or does not work). and the trials are independent.

Answer 2

The variable x is (approximately) a binomial random variable because (B) there are only two possible outcomes on each trial

How to determine the true statement?

The proportion that do not work on summer vacation is given as:

p = 25%

This means that the proportion that work on summer vacation is

q = 75%

Binomial variables can only take any of two possible outcomes, and each outcome is independent

This means that the variable x is (approximately) a binomial random variable because (B)

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