STAT200 MIDTERM EXAM Name:______________________
Your work should be neat and organized. Incomplete answers or work that is difficult to follow will result in point deductions. You may include additional attachments with your work for the problems. The answers should be clearly labeled and matched with the problem number.
1. The U.S. Census Bureau needs to estimate the median income of males in the U.S., they collect incomes from 2500 males. State the individual, variable, population, sample, parameter, and statistic.
2. What does the standard deviation measure?
3. How many ways are there to select a president, vice president, and secretary from a class of 35 people?
4. How many different license plates are there that start with two letters followed by four digits? Assume there are no restrictions.
5. Describe the process and give a clear example for each of the following.
a. Stratified Sampling
b. Cluster Sampling
6. The Affordable Care Act created a market place for individuals to purchase health care plans. In 2014, the premiums for a 27 year old for the bronze level health insurance are given in the table. (“Health insurance marketplace, “2013). Create a frequency distribution, relative frequency distribution, and a cumulative frequency distribution. You should include all of these in the same distribution table.
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7. Using the same data as in problem 6, create a histogram and a relative frequency histogram. Describe the shape and any findings from the graph.
8. The probabilities that workers have 0, 1,2,3 cars are 0.05, 0.45, 0.35, and 0.15 respectively.
a. Construct a probability distribution
b. Find the expected value.
9. Say which level of measure (ordinal, ratio, interval, nominal) is being used for each of the following:
a. Height is measured in centimeters.
b. Students are given grades of A,B,C,D, or F on this exam.
c. Applicants are categorized by ethnic background.
10. The following data shows the number of years that a particular car lasts without needing an engine or transmission replacement. Construct a boxplot for the following data and comment on the shape of the distribution.
8, 12, 7, 3, 15, 9, 11, 11
11. The following table contains the number of M&M’s of each color that were found in a case (Madison, 2013).
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a. Find the probability of choosing a green or red M&M.
b. Find the probability of not choosing a brown M&M.
12. A community college accepts 80% of its applicants. Find the probability that exactly 3 out of 5 applicants are accepted.
13. What is the sample space of an experiment?
14. A statistics class has the following activities and weights for determining a grade in the course: test 1 worth 15% of the grade, test 2 worth 15% of the grade, test 3 worth 15% of the grade, homework worth 10% of the grade, semester project worth 20% of the grade, and the final exam worth 25% of the grade. If a student receives a 92 on test 1, an 85 on test 2, a 95 on test 3, a 92 on the homework, a 55 on the project, and an 83 on the final, what grade did the student earn in the class?
15. How is this class going?
Data of Health Insurance Premiums
M&M Distribution