Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find

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Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 74 and 84 questions

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Samantha 1 week 2021-09-10T12:29:00+00:00 1 Answer 0

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    2021-09-10T12:30:59+00:00

    Answer: 0.7264

    Explanation:

    The number of independent questions (n)  = 100

    Probability of answering a question (p) = 0.80

    Let X be the no. of questions that need to be answered.

    \therefore random variable X follows binomial distribution

    The probability function of a binomial distribution is given as

    P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}

    Now , we nee to find P(74 ≤ X ≤ 84)

    \therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)

    P(74 ≤ X ≤ 84) = \sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}

    P(74 ≤ X ≤ 84) = 0.7264

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