Explore BrainMass

Explore BrainMass

    Normal Probability

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please explain solutions for #21, 22.

    A final Math exam has a normal distribution with mean 73 and standard deviation 3.5.

    21- If one student is randomly selected, find the probability that his score be less than 71:

    A) 0.7158 B) 0.2843 C) 0.4934 D) 0.6432

    22- If 25 students are randomly selected, find the probability that the mean of their scores be less than 71:

    A) 0.9930 B) 0.9979 C) 0.0021 D) 0.0021

    23- Why can the Central Limit be applied in question #22, if the sample size doesn't exceed 30?

    A) Because the theorem is easy to apply
    B) Because the population has a Normal distribution
    C) Because this theorem is very important in inferential statistics.
    D) Because this theorem apply only in scores distributions.

    © BrainMass Inc. brainmass.com October 4, 2022, 3:27 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/probability-distributions-math-exam-scores-414559

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attachment.

    Probability Math Exam
    A final Math exam has a normal distribution with mean 73 and standard deviation 3.5.

    21- If one student is randomly selected, find the probability that his score be less than 71:

    A) 0.7158 B) 0.2843 C) 0.4934 D) 0.6432
    Hint:
    Let X be the score obtained in the final Math exam. Given that X is normal with mean µ = 73 and standard deviation  = 3.5.
    We need P (X < 71). Standardizing the variable X using and from standard normal tables, we have
    P (X < 71) = = P (Z < -0.57) = 0.2843

    22- If 25 students are randomly selected, find the probability that the mean of their scores be less than 71:

    A) 0.9930 B) 0.9979 C) 0.0021 D) 0.0021
    Hint:
    Since X ~ N (µ, σ), . That is, or ~ N (73, 0.7). Standardizing using and from standard normal tables, we have,
    P ( < 71) = = P (Z < -2.86) = 0.0021

    23- Why can the Central Limit be applied in question #22, if the sample size doesn't exceed 30?

    A) Because the theorem is easy to apply
    B) Because the population has a Normal distribution
    C) Because this theorem is very important in inferential statistics.
    D) Because this theorem apply only in scores distributions.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 4, 2022, 3:27 pm ad1c9bdddf>
    https://brainmass.com/statistics/probability/probability-distributions-math-exam-scores-414559

    Attachments

    ADVERTISEMENT