Question

Determine whether the given procedure meets the criteria of a binomial distribution? If not, identify one requirement that is noit satisfied. 1. A survey of college students rating the food in the campus dining hall on a scale from 1-10. 2. Surveying 124 people living in the United States who use Internet service and recording their 'no' responses to the question."Do you think that internet sites should be federally regulated"? 3. Spinning a roulette wheel nine times and recording the number of times the ball lands on black. 4. Spinning the roulette wheel nine times and recording the number that the ball lands on.

Answer 1

A binomial experiment is a statistical experiment that has the following properties:

• The experiment consists of n repeated trials.
• Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
• The probability of success, denoted by P, is the same on every trial.
• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

1. A survey of college students rating the food in the campus dining hall on a scale from 1-10.

This does not meets the criteria of a binomial distribution, because there are 10 possible outcomes (instead of 2) for each student (trial).

2. Surveying 124 people living in the United States who use Internet service and recording their 'no' responses to the question."Do you think that internet sites should be federally regulated"?

There are fixed 124 trials. There are two possible outcomes - responses recorded (when the resonse is 'no') or no response recorded. But, the probability of success ('no' response) is not the same for every people as the people opinions may differ. So, this does not meets the criteria of a binomial distribution.

3. Spinning a roulette wheel nine times and recording the number of times the ball lands on black.

This does not meets the criteria of a binomial distribution, because there are 9 possible outcomes (instead of 2) for each spin (trial).

4. Spinning the roulette wheel nine times and recording the number that the ball lands on.

Let x be the total numbers on roulette wheel. This does not meets the criteria of a binomial distribution, because there are x possible outcomes (instead of 2) for each spin (trial).