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Students are asked to write a 250-word essay and a spell-checker is used to count the number of spelling errors. Let the random variable be the number of spelling errors in an essay. Is the number of spelling errors in an essay a binomial random variable? Select all that apply.

Yes. All four conditions are met.
No. There is not a fixed number of trials.
No. The trials cannot reasonably be assumed to be independent.
No. The outcomes cannot be described as only "success" and "failure."
No. The probability of success is not the same for each trial.

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joaobezerra joaobezerra · Answer 1 · 2021-10-04T12:37:46+02:00

Using the conditions for the binomial distribution, it is found that it is a binomial variable, thus, the correct option is:

Yes. All four conditions are met.

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For a variable to be classified as binomial, four conditions have to be met.

For each trial, there can be only two possible outcomes.
There is a fixed number of trials.
Trials are independent.
In each trial, the probability of a success and a failure has to be the same.

In this problem, the random variable is the number of spelling errors, which is a binomial variable, as:

There are 250 words, thus the number of trials is fixed.
For each word, either there is a spelling error or not, thus two possible outcomes.
The probability of a word being misspelled is independent of any other word, that is, the probability of an spelling error is the same.

Thus, the correct option is:

Yes. All four conditions are met.

A similar problem is given at https://brainly.com/question/21772486