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An experiment consists of 400 observations and four mutually exclusive groups. If the probability of a randomly selected item being classified into any of the four groups is equal, then the expected number of items that will be classified into group 1 is ________.

User TokyoToo
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1 Answer

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Answer:

The expected number of items that will be classified into group 1 is 100.

Explanation:

For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

The expected value of the binomial distribution is:


E(X) = np

400 observations

This means that
n = 400

Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.

This means that
p = 0.25

Then the expected number of items that will be classified into group 1 is


E(X) = np = 400*0.25 = 100

100 is the answer.

User Vitalizzare
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