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Exam 1 - Review

# Exam 1 - Review - Statistics 321 Exam 1 Review Disclaimer...

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Unformatted text preview: Statistics 321: Exam 1 Review Disclaimer: This review is not meant to reflect the actual exam or all of the material covered in class. This is only meant to serve as an aid when studying for the test. 1. A state energy agency sends questionnaires to homeowners. When the surveys are returned, one survey is picked randomly. Define the events: A: {The home is constructed of brick} B: {The home is more than 30 years old} C: {The home is heated with oil} Describe the following events in terms of unions, intersections, and complements, then draw a Venn diagram and shade the appropriate region. a. The home is more than 30 yrs. old and heated with oil. b. The home is not constructed of brick. c. The home is heated with oil or more than 30 yrs. old. d. The home is constructed of brick and is not heated w/ oil. 2. Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a. Draw a tree diagram showing the probabilities. b. Are what happens to the first flight and what happens to the luggage independent events? c. What is the probability that the luggage arrives on time in Denver? 3. A local bank is reviewing its credit card policy. In the past, 5% of cardholders have defaulted on payments. The bank has found that the probability of missing one or more monthly payments is 20% for customers who do not default. (Of course, the probability of missing one or more payments is 100% for those who do default.) If a customer misses a monthly payment, what is the probability that they will default on their credit card? 4. In a survey of 1,929 MBA students, the following data were obtained on "students' first reason for application to the school they entered". The reasons cited were school quality, cost or convenience, or other reasons. Reason for Application Quality Cost/Conv. Other Total 890 421 393 76 Enrollment Full-Time 400 593 46 1039 Status Part-Time 821 986 122 1929 Total F = student is fulltime P = student is parttime Q = student applied because of school quality CC = student applied because of cost or convenience O = student applied for other reasons Find the probability that a. A randomly selected student is a fulltime? b. A student is full time and applied for the quality of education? c. A student who applied for cost/convenience is enrolled parttime? 5. You pick a random card from a deck. A = the card is an ace D = the card is a diamond F = the card is a face card (Jack, Queen, or King) a. What are P(A), P(D), and P(F)? b. Are A and D mutually exclusive events? c. Are D and F mutually exclusive events? d. Are A and F mutually exclusive events? e. What is the probability of drawing an ace or a face card? f. What is the probability of drawing an ace or a diamond? g. What is the probability of drawing a diamond or face card? h. What is the prob. of drawing an ace, diamond or face card 6. At an electronics plant, it is known from past experience that the probability is 0.86 that a new worker who has attended the company's training program will meet the production quota and that the corresponding probability is 0.35 for a new worker who had not attended the company's training program. Eighty percent of all new workers attend the training program. a. What percent of the new workers have attended the company's training program and met production quota? b. What is the probability that a new worker will meet the production quota? c. If a new worker has met production quota, what is the probability that he/she attended the company's training program? 7. A local clothing store keeps track of individual customer purchase amounts and has determined that, for those individuals who actually buy something, the mean amount spent is \$190 and the standard deviation is \$60. What can we say about the proportion of customers who spend between \$70 and \$310? 8. From the text: Section 2.4: 9, 10, 11, 19, 25 Section 2.5: 1, 3, 5, 9 ...
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