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# Probability Distributions, Scatter Plot and Regression

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1. A bag of colored blocks contains the following assortment of colors:
red (15), blue (6), orange (22), purple (14), green (6), and yellow (17).

Construct the probability distribution for x.

2. Classify the following as discrete or continuous random variables.

(A) The number of criminal justice majors at South University
(B) The weight of bags of apples, with 20 apples in a bag
(C) The number of fractions between 1 and 2
(D) The length of a broad jump

3. In testing a new drug, researchers found that 10% of all patients using it will have a mild side effect. A random sample of 14 patients using the drug is selected. Find the probability that:

(A) exactly two will have this mild side effect
(B) at least three will have this mild side effect.

4. Find the mean and standard deviation of the following probability distribution:

x 1 2 3
P(x) 0.1 0.6 0.3

5. Construct a scatterplot for the (x, y) values below, and answer the following questions. You do NOT need to submit your scatterplot with your answer; however, show all other work.
x y
1 7.0
2 13.0
3 19.0
4 25.0
5 31.0

- What would be the slope of this regression line?
- Would the correlation between x and y be positive or negative?
- How would you interpret these data in terms of linear regression?

? What percentage of the grand total of students are males in the criminal justice program?
? Which programs tend to have more males than females in them?
? List the percentages of students in each major area as compared to the grand total.

7. How many green elements are required to make this a legitimate probability distribution if there are a total of 50 elements in this sample?
x red blue orange brown green
P(x) 0.20 0.20 0.20 0.20