Discuss the below in detail:
1. Describe exactly what information is provided by a Z-score
2. A distribution has a standard deviation of σ=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 σ=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
4. 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
6. The distribution of SAT scores is normal with φ=500 and σ=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?