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Ralphie is taking a ten-question multiple choice test. Each question has five choices. If Ralphie answers a question
correctly, he earns one point; if he answers incorrectly, he loses half a point. Ralphie answers the first six questions
correctly, then guesses on the last four. What is the expected value of his test score? Round the answer to the nearest
whole percent.

Sagot :

Using the binomial distribution, it is found that the expected value of his test score is of 6.8.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem, the parameters are given as follows:

  • For the first 6 questions, n = 6 and p = 1.
  • For the last 4 questions, n = 4 and p = 1/5 = 0.2.

Hence, the expected score is given by:

E(X) = 6 x 1 + 4 x 0.2 = 6.8.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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Answer:

A.

Step-by-step explanation:

View image 329758
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