# 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.

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?

#### Solution Summary

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