A random sample of 320 people is selected from a large city. A poll is conducted to determine how many people in the sample regularly watch cable news channels. Each person is asked to respond with either a yes or a no. a. The outcome of each trial is independent of those of other trials. b. Each trial has only two possible (mutually exclusive) outcomes. c. The probability of each possible outcome in any trial is the same from trial to trial. d. There is a fixed number of n trials. This example ___ a binomial experiment.

Question

Mathematics

Cayden Boone

14 February, 11:07

A random sample of 320 people is selected from a large city. A poll is conducted to determine how many people in the sample regularly watch cable news channels. Each person is asked to respond with either a yes or a no. a. The outcome of each trial is independent of those of other trials. b. Each trial has only two possible (mutually exclusive) outcomes. c. The probability of each possible outcome in any trial is the same from trial to trial. d. There is a fixed number of n trials. This example ___ a binomial experiment.

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Answers (1)

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Elijah Giles · Answer 1

All the conditions are verified

This example is a binomial experiment.

Explanation:

This question first asks to determine which properties of a binomial experiment apply to a list of conditions (a. trhough d.), and, then, conclude wheter the example is or not a binomial experiment.

Conditions:

a. The outcome of each trial is independent of those of other trials.

This is correct because it assumes that the population is large and the fact that one member of the sample watches or does not watch the cable news channels does not change the fact that another member watches or does not watch the cable news channels.

For this assumption to be valid, the survey must not conducted on two or more people living in the same house, because, in that case, the fact that one member regularly watches cable news channels would affect the other members of the same house.

Therefore, under some ideal conditions, this statement is true.

b. Each trial has only two possible (mutually exclusive) outcomes.

This is correct.

Each person can only answer yes or not, because either the person regularly watches cable new channles or not. Both things cannot happen at the same time. Thus, they are mutually exclusive outcomes.

c. The probability of each possible outcome in any trial is the same from trial to trial.

Correct.

There is not distinction about the persons, thus the probability for each person surveyed (each trial) to answer yes or not is the same.

d. There is a fixed number of n trials.

Correct: the number of trials is 320, the size of the sample, and it does not change.

Conclusion

Since all the conditions are correct, this example is a binomial experiment.