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Math Help - Standard Deviation

  1. #1
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    Standard Deviation

    I need help with these two question from my practice final exam. I had trouble with these two problems on my midterm as well and need help knowing how to solve them.
    -A population is normally distributed with mean 28.9 and standard deviation 3.8.
    a) Find the intervals representing one, two, and three standard deviations from the mean.
    b) What percentage of the data lies in each of the intervals in (a) above.

    -The scores on a certain class exam are normally distibuted with mean score of 68 and standard deviation 9.
    a. What is the probability that a score is above 68.
    b. What is the probability that a score is below 68.
    c. What is the probability that a score is between 68 and 90.
    d. What is the probability that a score is above 85.
    e. What is the probability that a score is between 62 and 85.
    f. What is the minimum score requires to place in the top 5% of the class.
    g. A test with a score below ________ will place in the bottom 10% of the class.
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  2. #2
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    Quote Originally Posted by d.darbyshire
    I need help with these two question from my practice final exam. I had trouble with these two problems on my midterm as well and need help knowing how to solve them.
    -A population is normally distributed with mean 28.9 and standard deviation 3.8.
    a) Find the intervals representing one, two, and three standard deviations from the mean.
    b) What percentage of the data lies in each of the intervals in (a) above.
    .
    The first interval is,
    28.9-3.8,28.9+3.8
    Which is,
    25.1,32.7 This takes 68%
    The next interval is,
    25.1-3.8,32.7+3.8
    Which is,
    21.3,36.5 This takes 95%
    The next interval is,
    21.3-3.8,36.5+3.8
    Which is,
    17.5,40.3 This takes 99.7%
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  3. #3
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    Quote Originally Posted by d.darbyshire
    -The scores on a certain class exam are normally distibuted with mean score of 68 and standard deviation 9.
    a. What is the probability that a score is above 68.
    50% Because it is the middle.
    Quote Originally Posted by d.darbyshire
    b. What is the probability that a score is below 68.
    50% Because it is the middle also
    Quote Originally Posted by d.darbyshire
    c. What is the probability that a score is between 68 and 90.
    That is 2.44 standard deviations other, the z-score is, 49.27%
    Quote Originally Posted by d.darbyshire
    d. What is the probability that a score is above 85.
    Quote Originally Posted by d.darbyshire
    That is two standard deviations over approx 86, which is,
    44.5%
    Quote Originally Posted by d.darbyshire
    e. What is the probability that a score is between 62 and 85.
    12.93% below 68 and above 62 and 49.46% above 68 and below 85 which adds to 63.3%
    Quote Originally Posted by d.darbyshire
    f. What is the minimum score requires to place in the top 5% of the class.
    That mean it takes 45% over the 68 interval (middle) which is z=1.65 thus, the interval is 82.25
    Quote Originally Posted by d.darbyshire
    g. A test with a score below ________ will place in the bottom 10% of the class.
    That means the interval needs to be below 40% from the middle. Which happens when z=1.28 thus, the interval begins at (remember to subtract you are going other direction) 56.48
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