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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

https://brainmass.com/statistics/regression-analysis/probability-distributions-scatter-plot-and-regression-381873

#### Solution Summary

This solution provides formatted calculations, tables and charts in the attached Word document. A scatter plot is included in a second Word document.

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## Probability Distribution, Correlation & Regression Analysis

The scatter plot below shows the relationship between the day of a particular month a stock was valued and the price of the stock in dollars. The horizontal axis represents the day of the month. Use this graph to answer the questions below.

Please see the attachment for the scatter plot.

(A) How would you describe the relationship between the day of the month this stock was valued and the price of the stock?
(B) Approximately what was the stock price on day 8?
(C) Would the slope of the "line of best fit" be positive or negative?

2. Suppose we want to determine the (binomial) probability(p) of getting 6 heads in 12 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?

3. For the table that follows, answer the following questions:
x y
1 -3
2 -2
3 -1
4

Would the correlation between x and y in the table above be positive or negative?

Find the missing value of y in the table.

How would the values of this table be interpreted in terms of linear regression?

If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?

If the correlation coefficient is -0.54, what is the sign of the slope of the regression line?

As the correlation coefficient decreases from 0.86 to 0.81, do the points of the scatter plot move toward the regression line, or away from it?

6. Determine whether each of the distributions given below represents a probability distribution and justify your answer.

(A)

x 1 2 3 4
P(x) 3/8 1/12 7/24 1/3

(B)

x 3 6 8
P(x) 2/25 .1 4/5

(C)

x 20 35 40 50
P(x) 0.54 0.12 -0.03 0.37

7. Three socks are selected, one at a time from a clothes drawer containing 6 black, 6 brown and 6 green socks. Let x represent the number of brown socks selected in 3 selections from the drawer.

(A) If this experiment is completed without replacing the socks each time, explain why x is not a binomial random variable.
(B) If this experiment is completed with replacement of the socks each time, explain why x is a binomial random variable

8. You are given the following data.
Number of Absences Final