Download 14 Questions for Past Exam 1 - Elementary Statistical Methods I | STAT 211 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity!
Statistics 211 Name ______________________________
Exam I Student # _____________ ________
February 14, 2007 Instructor ___________________________
Time of Class ________________________
INSTRUCTIONS:
1. Make sure you have 7 pages and 14 problems.
2. DO ALL WORK ON THE ATTACHED PAGES.
3. For all questions, ALL WORK MUST BE SHOWN in order to receive full credit. This
includes, among others, NOTATION, DEFINITION OF EVENTS AND RANDOM
VARIABLES, PROBABILITY STATEMENTS and CORRECT ANSWERS.
4. Some problems require numerical answers. For these problems, space is provided where
you MUST write your final answer.
5. Points for each section are indicated in the brackets.
6. You may keep your numerical answer in either fractional form or decimal form. If using
decimal form, round your answer to 4 decimal places.
Scoring Summary
Problems
Possible
Points Earned Points
1 17.5 ___________
2 14 ___________
3 14.5 ___________
4 6.5 ___________
5 7 ___________
6 12 ___________
7 6 ___________
8 8 ___________
9 -14 14.5 ___________
Total 100
- [3+3+3+5.5+3] The Ohio Lottery is currently offering an instant game called Valentine’s Day Doubler. With this game, the ticket prizes range from $1 to $100. Shown here are the various prizes and the probability of winning each prize:
Prize: x $0 $1 $2 $10 $50 $ Probability: p(x) 0.770 0.150 0.050 0.025 0.004 0.
a. If you buy one ticket, what is the probability that you will win a prize?
Answer _____________
b. If you buy one ticket, what is the probability that you will win no more than $10?
Answer _____________
c. If you buy one ticket, what is your expected winning prize amount?
Answer _____________
d. What is the standard deviation of the winning prize amount?
Answer _____________
e. If each ticket costs $1 and you buy one ticket, what is your expected profit?
Answer _____________
- [5+3+3+3.5] Since the day his son played his first baseball game, Myson Gewdursnot has been boasting about how well his boy, Imso Gewdursnot, could play the game. Myson just knew his son would play in the Big Leagues one day. Well, Myson’s neighbor, Will Eweshutit, had heard enough of this bragging and boasting and decided to throw some statistics at Myson Gewdursnot. Upon searching the Web, Will discovered that only 14% of the boys that play baseball in high school go on to play in college (C). Also, of those boys who play baseball in college, only 11% go on to play professional baseball (M). And even rarer, only one half of a percent (0.5% = 0.005) of the boys that play baseball in high school and do play not in college go on to play professional baseball.
a. Construct a probability tree. Be sure to list the simple events and their corresponding probabilities.
b. What is the probability that Imso will not play baseball after high school?
Answer _____________
c. What is the probability that Imso will not play professional baseball?
Answer _____________
d. Suppose that a professional baseball player is randomly selected. What is the probability that he did not play college baseball?
Answer _____________
- [3+3.5] For each day of the past year, the number of vehicles passing through a certain intersection was recorded by a city engineer. This information will be used to determine if a traffic light needs to be installed at this intersection. Suppose the distribution of the number of vehicles passing through the intersection per day is mound shaped with a mean of 775 vehicles per day and a standard deviation of 25 vehicles per day.
a. For what percentage of days did at least 725 vehicles but no more than 800 cars use the intersection?
Answer _____________
b. On approximately how many days last year did no more than 725 vehicles use this intersection (assuming there were 365 days last year).
Answer _____________
- [3.5+3.5] Based on a demand analysis forecast, a factory plans to produce 800,000 DVDs this quarter, on average, with an estimated uncertainty of 5,000 DVDs as the standard deviation. A fixed equipment cost of $73,000 must be paid each quarter. Also, a variable cost of $0.62 must be paid for every DVD produced during the quarter. Let X = the number of DVDs produced during the quarter.
a.. Based on the forecast, what is the expected total cost of the DVDs produced for the quarter?
Answer _____________
b. What is the uncertainty involved in this forecast of the total cost of the DVDs produced for the quarter, expressed as a variance?
Answer _____________
- [3+3] A local company took applications from graduating BGSU business majors at a recent job fair. After looking at the transcripts of these BGSU applicants, it was noted that 18% had earned a grade of ‘B’ or better in STAT 211. The company eventually hired 25% of these applicants. Furthermore, 13% both were hired and earned a ‘B’ or better in STAT 211. Let H = the event that the applicant was hired and B = the event that the applicant earned a grade of ‘B’ or better in STAT 211.
a. What is the probability that a randomly selected hired applicant earned a grade of ‘B’ or better in STAT 211?
Answer _____________
b. What is the probability that a randomly selected hired applicant did not earn a grade of ‘B’ or better in STAT 211?
Answer _____________
- [3+3+2] You have determined that 4.3% of the CDs that your factory manufactures are defective due to a problem with materials (M) and that 2.4% are defective due to human error (E). Assume that these two events are independent.
a. Find the probability that a randomly selected CD will have at least one of these defects.
Answer _____________
b. What is the probability that a randomly selected CD will have neither of these defects?
Answer _____________
c. Suppose that a randomly selected CD has a defect due to human error. Knowing this, what is the probability that the CD has a defect due to a problem with materials?
Answer _____________
- [1.5+1.5+1.5] In the space provided in front of the three terms listed below, write in the letter corresponding to the most appropriate definition.
________ Descriptive statistics ________ Parameter ________ Sample
Definitions:
(a) a descriptive measure of a population
(b) the crossbeam used to secure a widget to a gersnaffle
(c) a body of methods used to draw conclusions about characteristics of populations based on sample data
(d) methods of organizing, summarizing, and presenting data in a convenient and informative way
(e) a descriptive measure of a sample
(f) a set of data drawn from the population
(g) the group of all items of interest to a statistics practitioner
- [1.5] Determine if the following random variable is discrete or continuous. Circle the correct answer.
The time in seconds it takes for a person’s heart to beat 20 times after running up three flights of stairs.
a. discrete random variable b. continuous random variable
- [2] It is possible for two events to be both mutually exclusive and independent. Circle the correct answer.
a. TRUE b. FALSE
- [1.5+1.5] The prices (in dollars) of a sample of ten different brand names of toothpaste were observed. The following information was calculated: ∑ x = 21.03 (the sum of the observations) and ∑ x 2 = 45.50 (the sum of the squared observations). Circle the correct answer for both parts.
a. If we replace a toothpaste in the sample that costs $1.50 with another toothpaste that costs $2.50, what would happen to the population mean price of toothpaste?
(i) increase (ii) decrease (iii) stay the same (iv) Not enough information given.
b. If we replace a toothpaste in the sample that costs $1.50 with another toothpaste that costs $2.50, what would happen to the sample variance of the prices?
(i) increase (ii) decrease (iii) stay the same (iv) Not enough information given.
- [2] Circle the correct answer. Which of the following is a unimodal, positively-skewed (right-skewed) histogram?
(a) (b) (c) (d)
- [1.5] Determine if the following data are qualitative (nominal or ordinal) or quantitative (interval). Circle the correct answer.
Political affiliation (e.g., Republican, Democrat, Libertarian, Independent, Other)
a. qualitative b. quantitative
