Probability & Statistics Final Exam Open Ended Review

Probability & Statistics – Final Exam Review

1. The state gas tax (in cents) for 25 states is given below.

a. Construct a frequency distribution table with 5 classes. b. Use this frequency distribution table to create a histogram for the data. c. Find the mean, standard deviation, 5-number summary and IQR d. Create a boxplot for the data. e. Which amount would correspond to the 75th percentile?

7.5 16 23.5 17 22 21.5 19 20 27.1 20 22 20.7 17

28 20 23 18.5 25.3 24 31 14.5 25.9 18 30 31.5

2. Use the following data to construct a boxplot and then test to see if there are any outliers:

89 47 164 296 30 215 138 78 48 39

3. A package contains 12 resistors, 3 of which are defective. If 4 are selected at random, find the probability of getting:

a. 0 defective resistors b. At least 1 defective resistor c. All defects

4. How can you tell the general shape of a distribution [symmetric or skewed] if all you know if the mean and median of the distribution?

5. An insurance company insures a person’s vehicle for $32,000 for an annual premium of $1,200. We will simplify things by considering the following two outcomes: If the company figures that the probability of the car being totaled is .0325 and the probability of paying $5000 for a minor accident is .1152, what will be the company’s expected profit?

6. Each month, an American household generates an average of 28 pounds of recyclables for garbage. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of generating: a. Between 27 and 31 pounds per month b. More than 30.2 pounds per month

Assume the variable is normally distributed.

7. Define or describe the following : a. Inferential Statistics & Descriptive Statistics b. Data collection methods c. Rounding rule for reporting statistics d. Qualitative & Quantitative Variables [continuous & discrete too] 8. Answer the following questions involving correlation and regression:

a. The correlation coefficient r can be any value between _____ and _____.

b. When all points fall on the regression line, the value of the correlation coefficient would be r = _____.

c. When a correlation is weak, r is close to _____.

d. When a correlation is strong [and negative], r is close to _____.

e. What does the coefficient of determination [ ] tells us?

f. A statistical graph of two quantitative variables is called a ______.

g. Another name for the x-variable is the ______variable.

h. Another name for the y-variable is the ______variable.

i. What is the study of linear regression used for in the practice of statistics?

9. Find the weighted mean (GPA) of this student’s fall semester.

Course Credits Grade Points

English Composition 3 3.5

Calculus 4 2.8

Psychology 3 3.0

Sociology 3 4.0

10. Find the z-scores for the following tests and state which one the student did better on relative to his/her classmates.

Test A Score = 45 Mean = 48 S = 5

Test B Score = 80 Mean = 93 S = 10

11. Perform a linear regression analysis to predict sales from $ spent on advertising.

Month 1 2 3 4 5 6 7 8 9 10 11 12

Advertising $ 5.5 5.8 6 5.9 6.2 6.3 6.5 6.6 6.4 6.5 6.7 6.8 (1000s)

Sales 100 110 112 115 117 116 118 120 121 120 117 123 (1000s)