statistics

Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. Estimate the probability that among 75 randomly selscted students, at least 20 of them score greater that 78.

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asked by Jean
  1. Use z-scores.

    z = (x - mean)/sd

    With your data:

    z = (78 - 68.2)/10.4 = 0.94

    .1736 is the probability using a z-table for a single student with a score greater than 78.

    Now we can use a normal approximation to the binomial distribution.

    mean = np = (75)(.1736) = 13
    standard deviation = √np(1-p) = √(75)(.1736)(.8264) = 3.28

    Again, use z-scores.
    z = (20 - 13)/3.28 = 2.13

    Use the z-table to find the probability. (Remember the problem says "at least 20" which means 20 or more.)

    I hope this will help.

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