Probability, Normal distribution problems
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.
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.
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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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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