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Math Help - Normal Distribution

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    Normal Distribution

    Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.

    1. What is the probability that x is greater than 8.5?

    2. What is the probability that x is greater than 6.5?

    3. What is the probability that x is greater than 3 but less than 5.5?

    4. What is the probability that x is less than 7.5?
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    Quote Originally Posted by Jdavis6023 View Post
    Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.

    1. What is the probability that x is greater than 8.5?
    8.5 is 1 away from 7.5, so you are .33 of a standard deviation away from your mean. a normal distribution table gives a value of .1293 for .33, so your probability is 12.93%.

    2. What is the probability that x is greater than 6.5?
    6.5 is also 1 away from 7.5, but now you're talking about everything greater than something below your mean- you'll have more than half the data. So, instead of .1293, you want .8707 (everything else)

    3. What is the probability that x is greater than 3 but less than 5.5?
    Find two probabilities here, then subtract.

    4. What is the probability that x is less than 7.5?
    In a normal distribution, what percent of data are above the mean?
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    Hello,
    Quote Originally Posted by Jdavis6023 View Post
    Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.
    Let Z=\frac{X-7.5}{3}
    Z follows a standard normal distribution.

    1. What is the probability that x is greater than 8.5?
    \mathbb{P}(X > 8.5)=\mathbb{P} \left(Z > \frac{8.5-7.5}{3}\right)=1-\mathbb{P} \left(Z<\frac{8.5-7.5}{3}\right)

    2. What is the probability that x is greater than 6.5?
    \mathbb{P}(X > 6.5)=\mathbb{P} \left(Z > \frac{6.5-7.5}{3}\right)=1-\mathbb{P}\left(Z<\frac{6.5-7.5}{3}\right)

    3. What is the probability that x is greater than 3 but less than 5.5?
    \mathbb{P}(3<X<5.5)=\mathbb{P} \left(\frac{3-7.5}{3}<Z <\frac{5.5-7.5}{3}\right)= \mathbb{P} \left(Z<\frac{5.5-7.5}{3}\right)-\mathbb{P}\left(Z<\frac{3-7.5}{3}\right)

    4. What is the probability that x is less than 7.5?
    This makes Z<0, which is... ?



    Use a z-table : http://www.science.mcmaster.ca/psych...e/z-table2.jpg
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