Statistics
Mohsin
stat.pdf
Max Point: 100 Name__________________________________________Student #____________________________Date__________ Score________ Instructions: Read each problem carefully, write neatly, and respond to all problems. Show all work, wherever necessary. Students are required to work on this test independently. Do not share your solutions/answers with fellow classmates during the time period of this test. Calculator and Computer are allowed. PART I Multiple Choice Problems: Circle the letter of the most appropriate option or best choice for each problem. (30 points) 1) Each year, in a small town in Maryland, an award is given to the person who has read the most books in a year. The following is a table representing the ages of the book award winners over the past 30 years. Ages of Book Award winners over the past 30 years: 41 34 51 62 32 42 54 52 30 39 53 44 29 43 56 35 51 57 28 30 30 53 41 34 51 62 43 32 42 50 What age range is the winner most likely to be in? A) 56 – 65 B) 46 – 55 C) 36 – 45 D) 26 – 35 2) Suppose that in an assortment of 20 blackberries, there are 5 with defective switches. In a draw without replacement, if 3 blackberries are picked at random, what is the probability that all 3 have defective switches? A) 0.250000 B) 0.008772 C) 0.015625 D) None of the above The Brown family has 3 girls. 3) What is the probability of a 3-‐child family having 3 girls? A) 0.5000 B) 0.0125 C) 0.0625 D) 0.1250 4) What is the probability that the next child of the Brown family will be a girl, given that they have already 3 girls in a row? A) 0.50000 B) 0.25000 C) 0.06250 D) 0.03125
Please refer to the following table for Questions 5 through 8. Temperatures in the first 2 weeks of July in a town in Virginia. Date Temperature July 1 94 July 2 84 July 3 99 July 4 92 July 5 88 July 6 84 July 7 86 July 8 78 July 9 76 July 10 74 July 11 88 July 12 82 July 13 84 July 14 88 5) Which of the following stem-‐and-‐leaf diagrams best represents the temperatures of these 14 days, constructed with 2 lines per stem? ________ A) 9 | 2 4 9 8 | 6 8 8 8 8 | 2 4 4 4 7 | 4 6 8 B) 9 | 2 4 9 8 | 2 4 4 4 6 8 8 8 7 | 4 6 8 C) 9 | 9 9 | 2 4 8 | 6 8 8 8 8 | 2 4 4 4 7 | 6 8 7 | 4 D) 9 | 4 9 9 | 2 8 | 4 4 4 6 8 8 8 8 | 2 7 | 6 8 7 | 4 3 6) What is the distribution shape of the temperatures listed above? ________ A) Right skewed B) Normally distributed C) Left skewed D) None of the above
7) What is the mean temperature for the above data?________ A) 85.5 B) 85.0 C) 90.5 D) 86.7 8) A random sample of 5 dates is selected and a standard deviation is calculated for these 5 dates. The dates and the respective temperatures are: Date Temperature July 1 94 July 3 99 July 8 78 July 11 88 July 14 88 What is the standard deviation of these values? ________ A) 8.23 B) 6.44 C) 7.86 D) 12.80 9) The following data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Democrat given that a male was selected? Republicans Democrats Independents Male 20 24 6 Female 36 19 3 _______ A) 0.222 B) 0.480 C) 0.500 D) 0.414 10. A teacher gives a 20-‐point test to students. The scores are listed below. What percentile corresponds to the score of 12? 20 8 10 7 15 16 12 19 14 9
A) 12 B) 25 C) 13 D) 40 E) None
11. “The probability that a newborn baby is a girl is ½.” Classify the statement as an example of A) Empirical probability B) Classical probability C) Subjective probability D) None 12. A question has five multiple-‐choice answers. Find the probability of guessing an correct answer. A) 5/2 B) 4/5 C) 1/5 D) 3/5 E) None 13. The P(A) = 2/5. Find the odds in favor of A. A) 2 to 3 B) 2 to 5 C) 5 to 2 D) 3 to 2 E ) None 14. Given events A and B, where P(A) = 0.6, P(B) = 0.7, and P (A and B) = 0.30. Classify the events as A) Dependent B) Independent C) Mutually Exclusive D) None
15. The mean age of the students in your statistics class is 20 years. This statement describes: A) Descriptive statistics B) Inferential statistics C) Exploratory statistics D) None 16. The data reflecting the number of seats in each movie theater in Prince George’s County, Maryland, during FY 2013 is classified as
A) Quantitative data B) Qualitative data C) Continuous data D) None
17. Identify the level of measurement for data that are the number of pages in various college elementary statistics books on Amazon.com.
A) Ratio B) Ordinal C) Interval D) Nominal E) None
18. What method of data collection would you use to collect data for a study where a drug was given to 10 patients and a placebo to another group of 10 patients to determine if the drug has an effect on a patient’s illness?
A) Take a census B) Use sampling C) Use a simulation D) Perform an experiment E) None
19. A college student interviews everyone in his statistics class to determine who owns a car. What sampling technique is used?
A) Cluster B) Random C) Convenience D) Systematic E) Stratified
20-‐26: Given the following frequency distribution Miles (per day) | Frequency 1-‐2 | 9 3-‐4 | 22 5-‐6 | 28 7-‐8 | 15 9-‐10 | 4 20. Identify the class width used in the frequency distribution. A) 0 B) 1 C) 2 D) 3 E) 9 21. Identify the midpoint of the first class. A) 5.5 B) 28 C) 5 D) 1.5 E) None 22-‐23: For the stem-‐and-‐leaf plot below, Stem | Leaf 1 | 1 3 4 5 1 | 6 6 6 7 8 9 2 | 0 1 1 2 3 4 4 5 6 6 2 | 7 7 7 8 8 9 9 9 3 | 0 1 1 2 3 4 4 5 5 3 | 6 6 6 7 8 8 9 9 4 | 0 1 4 5 4 | 6 7 7 9 5 | 3 4 5 22. What is the maximum and what is the minimum entry? A) Max: 53; Min: 15 B) Max: 5; Min: 1 C) Max: 55; Min: 11 D) Max: 54; Min: 11 E) None
23. Find the range of the data set. A) 42 B) 44 C) 40 D) 11 E) None 24. Find the probability of answering three true or false questions correctly if random guesses are made. Only one of the choices is correct.
A) 0.25 B) 0.5 C) 0.75 D) 0.1 E) None
25. The events A and B are disjoint. If P(A) = 0.3 and P(B) = 0.2 what is P(A or B)? A) 0.5 B) 0.6 C) 0.06 D) 0.09 E) None 26. The probability that a salmon swims successfully through a dam is 0.70. Find the probability that two salmon swim successfully through the dam.
A) 0.700 B) 0.490 C) 0.343 D) 0.140 E) None
27. The mean IQ of students in a particular statistics class is 100, with a standard deviation of 5. The distribution is roughly bell-‐shaped. Use the Empirical Rule to find the percentage of students with IQ below 105. A) 84% B) 34% C) 13.5% D) 16% E) None PART II Solve each of the following problems (40 points) 1. Identify the sample space of the probability experiment and list the outcomes of the event. (12 pts) Experiment: Tossing a fair coin four times Event A: Exactly two heads and two tails A. Sample Space of the Experiment: __________________________________________ B. List of Outcomes of the Event A: _______________________________________ C. Determine the probability of A:________________________________________ 2. Complete the expanded frequency distribution by showing the midpoint, relative frequency, and cumulative frequency for each class. (12 pts) Phone calls (per day) Class Interval Frequency Midpoint Relative Frequency Cumulative Frequency 8—11 18 12—15 23 16—19 38 20—23 47 24—27 32 3. The table below shows the approximate U.S. age distribution from 2000 Census. (6 pts) Age ≤19yr 20-‐34 35-‐39 60-‐84 ≥ 85 Population 29 21% 34% 15% 1% A. What is the probability that a randomly selected person in the U.S. will be less than 20 years old? ______________ B. What is the probability that a randomly selected person in the U.S. will be at least 20 years old? _______________
4. In a box of 20 parts, five of the parts are defective. Two parts are selected at random without replacement. (4 pts) A. Find the probability that both parts are defective. _________________ B. Find the probability that both parts are not defective. _________________ 5. Given the following probabilities: P(A)= 0.40, P(B) =0.30, P(A ∩ B) = 0.15. (6 pts) A. Find P(A U B) __________ B. Find P(B | A) __________
B) Find the complement of P(A or B) __________
PART III Solve each of the following problems. (30 points) 1. Find the expected net gain to the player for one play of the game. If x is the net gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. (10 points) A) In American roulette, the wheel has the 38 numbers 00, 0, 1, 2, …, 34, 35, and 36 marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional 35 dollars. Otherwise, the dollar is lost B) A charity organization is selling $1 raffle tickets as part of a fund-‐raising program. The first prize is $150, and the second prize is $100. The rest of the prizes are 3 $25 gift certificates. The number of tickets sold is 500. __________________________________ 2. A surgical technique is performed on eight patients. You are told there is a 90% chance of success. Find the probability that the surgery is successful for (4 points) A) exactly five patients ___________________________ B) less than five patients _______________________________ 3. Find the mean and standard deviation of the given probability distribution. (6 points) X | P(X) 0 | 0.1296 1 | 0.3456 2 | 0.3456 4 | 0.0265 Mean = ______________________ Standard Deviation = ________________
4. A contractor is considering a sale that promises a profit of $38,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected profit? (4 points) ____________________ 5. Use the binomial probability formula to find the probability of x successes in n trials given the probability p of success on a single trial. (6 points)
A) n = 12, x = 5, p = 0.25
_____________________________________ B) n = 12, x > 5, p = 0.25 ______________________________________ C) n = 12, x < 5, p = 0.25 _____________________________________
