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    Probability, Normal distribution problems

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    1. Describe exactly what information is provided by a Z-score

    2. A distribution has a standard deviation of Ï?=4. Find the z-score for each of the following locations in the distribution.
    a. Above the mean by 4 points
    b. Above the mean by 12 points
    c. Above the mean by 2 points
    d. Above the mean by 8 points

    3. A distribution has a standard deviation of Ï?=10. For each of the following z-scores, determine whether the location is above or below the mean and determine how many points away from the mean. For example, z=+1.00 corresponds to a location that is above the mean by 10 points.
    a. Z=+2.00
    b. Z=+0.50
    c. Z=-2.00
    d. Z=-1.50

    12. A score that is 10 points below the mean corresponds to a z-score of z=-2.00. What is the population standard deviation?

    1. In a psychology class of 90 students, there are 30 males and 60 females. Of the 30 men, only 5 are freshmen. Of the 60 women, 10 are freshmen. If you randomly sample an individual from this class,
    a. What is the probability of obtaining a female?
    b. What is the probability of obtaining a freshman?
    c. What is the probability of obtaining man freshman?
    2. A jar contains 20 red marbles and 30 blue marbles. If you select marbles from the jar using random sampling:
    a. What is the probability that the first marble you select will be red?
    b. If you take a sample of n=3 marbles and the first two are both blue, what is the probability that the third marble will be red?

    3. What requirements must be satisfied to have a random sample?

    4. What is sampling with replacement, and why is it used?

    5. For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the tail is to the right or the left of the line and find the proportion in the tail.
    a. Z=2.00
    b. Z=0.50
    c. Z=-1.00
    d. Z=-0.75

    17. The distribution of SAT scores is normal with Ï?=500 and Ï?=100.
    a. What SAT score, X value, separates the top 10% from the rest of the distribution?
    b. What SAT score, X value, separates the top 30% from the rest of the distribution?
    c. What SAT score, X value, separates the top 40% from the rest of the distribution?

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    https://brainmass.com/statistics/probability/probability-normal-distribution-problems-122383

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    Solution Summary

    The solution gives the details of calculation of probability for events and probability of events based on normal distribution and Z score.

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