Midterm Exam Solution Q1: TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) A population is the totality of items or things under consideration. Answer: True 2) A sample is the portion of the universe that is selected for analysis. Answer: True 3) A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it. Answer: True 4) A set data in which the mean, median, and mode are all equal is said to be a skewed distribution. Answer: False 5) The relative frequency is the frequency in each class divided by the total number of observations. Answer: True 6) The symbol Âľ is used to represent the sample mean. Answer: False 7) Ogives are plotted at the midpoints of the class groupings. Answer: False 8) A histogram can have gaps between the bars, whereas bar charts cannot have gaps. Answer: False 9) To determine the width of class interval, divide the number of class groups by the range of the data. Answer: False 10) The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9. Answer: False 11) In a set of numerical data, the value for Q3 can never be smaller than the value for Q1. Answer: True 12) A boxplot is a graphical representation of a 5-number summary. Answer: True 13) The collection of all the possible events is called a sample space. Answer: True 14) In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in the sample is = 600. Answer: True 15) The Z score of an observation can never be negative. Answer: False 16) If P(A and B) = 0, then A and B must be mutually exclusive. Answer: True 17) When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B). Answer: True 18) Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) = 0.4 Answer: False 19) Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) = 0.3. Answer: False 20) Another name for the mean of a probability distribution is its expected value. Answer: True 21) In a Poisson distribution, the mean and standard deviation are equal. Answer: False 22) The number of customers arriving at a department store in a 5-minute period has a Poisson distribution. Answer: True 23) The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution. Answer: False
Q2: The grade point averages for 40 students are listed below.
i) Construct a frequency distribution, a relative frequency distribution, and a cumulative frequency distribution using eight classes. Include the midpoints of the classes. Answer:
ii) Construct a frequency polygon using eight classes. Answer:
Q3: Explain the difference between class limits and class boundaries. Answer: Class limits determine which numbers can belong to that class. Class boundaries are the numbers that separate classes without forming gaps between them. Q4: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Use the histogram below to approximate the mode heart rate of adults in the gym.
A) 2 B) 42 Answer: C
C) 70
D) 55
2) A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student's mean score in the class? A) 85.6 B) 80.6 C) 90.6 D) 76.6 Answer: B 3) The lengths of phone calls from one household (in minutes) were 2, 4, 6, 7, and 8 minutes. Find the midrange for this data. A) 10 minutes B) 5 minutes C) 6 minutes D) 2 minutes Answer: B 4) The cost of five homes in a certain area is given.
Which measure of central tendency should be used? A) mean B) midrange C) mode D) median Answer: D 5) A group of students were asked if they carry a credit card. The responses are listed in the table.
If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places. A) 0.400 B) 0.600 C) 0.240 D) 0.393 Answer: A 6) Use Baye's Theorem to solve this problem, A paper bag contains two red balls and one blue ball. A plastic bag contains three blue balls and one red ball. A coin is tossed. If it falls heads up, the paper bag is selected and a ball is drawn. If the coin falls tails up, the plastic bag is selected and a ball is drawn. If a red ball is selected, what is the probability that it came from the paper bag? A) B) Answer: C
C)
D)