Practice Exam 1

Practice Exam 1 Math 338 Instruction for the Actual Exam You have 75 minutes to complete the exam. The exam is closed-book and note. A copy of the formula sheet, which was posted on Canvas, is supplied. You may also use a calculator, but using a computer or other electronic devices is prohibited. Please read the questions carefully and supply sufficient details supporting your answers. When applicable, use tables, tree diagrams, or other means to provide details, and list the formula you used for computations. Good Luck Discrete Probability Events 1) Let 𝑋 have a binomial distribution. Select any expression that is equal to 𝑃(9 ≤ 𝑋 ≤ 14) . a) P(X≤14)-P(X≤9) b) P(X≤14)-P(X<9) c) P(X≤14)-P(X≤8) d) P(X≤14.5)-P(X≤8.5) (b, c, d) Dot Plot 2) Which one of the following describes a dot plot? a) Visual display of numerical data organized into equal intervals. b) Representing the distribution of data using median, quartiles, and extremes. c) Visual display of data where each value is represented by a dot (or an x). d) Display of change in data over time (c)

Valid Lottery 3) A new lottery randomly selects winners form players who buy a ticket and pays them $100 with probability 𝑝 1 , $10 with probability 𝑝 2 , or $1 with probability 𝑝 3 . Losers get no money. The distribution of amount won can be shown as follows: Table 1. Winning Distribution of a New Lottery ? ? ? ? ? ? ? $100 $10 $1 $0 ? ? 𝑝 1 𝑝 2 𝑝 3 𝑝 4 Which of the following distribution choices are a valid distribution for the amount won by a player. Table 2. Distribution Choices for the New Lottery ???????????? ?????𝒆? ? ? ? ? ? ? ? ? ? 0.1 0.05 0.49 0.35 ? 0.05 0.25 0.05 0.75 ? 0.29 0.36 0.15 0.2 ? 0.01 0.49 −0.05 0.55 ? 0.17 0.33 0.14 0.36 a) Distribution Choice A b) Distribution Choice B c) Distribution Choice C d) Distribution Choice D e) Distribution Choice E (c, e) City Government (Sampling Method). 4) The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents? a) Survey a random sample of persons within each geographic region of the city. b) Survey every 8th person who walks into city hall on a given day. c) Survey the first 300 people listed in the town's telephone directory. d) Survey a random sample of employees at the old city hall. (a)

9) Find if there are any outliers. a) 10 sorted observations: 2.86, 3.24, 3.24, 3.3, 3.4, 3.4, 3.4, 3.5, 3.8, 3.8 Min = 2.86; Max = 3.8; Med=(3.4+3.4)/2=3.4 Q1=3.24, Q3=3.5 2.86…….3.24…3.4..3.5……3.8 b) IQR = 3.5-3.24= 0.26, 1.5IQR=1.5(0.26)=0.39 LF = 3.24-0.39 = 2.85 Min > LF => No outlier UF = 3.5 + 0.39 = 3.89 Max < UF => No Outlier New Lottery: Assume that the distribution of the amount won in the new lottery is: Table 3. Winning Distribution ? ? ? ? ? ? $100 0.05 ? $10 0.10 ? $1 0.25 ? $0 0.60 Use this information to answer the next two questions. 10) Calculate the mean winning amount. Round the response to 3 decimal place, if needed. 6.25 (with margin: 0) 11) What is the best pricing approach for the entity that sells this lottery tickets? Select an appropriate response: a) Price the ticket to be slightly more than the mean winning amount. b) Price the ticket to be slightly less than the mean winning amount. c) Let people bid on the tickets. d) Stop selling, people are always winning. (a)

Real Estate Sales in NYC (Bayes) 12) In Bronx, NYC, 10.4% of real estate sales in 2020 has been commercial buildings, 59.6% of them are selling for more than $200/sq.ft. The proportion of residential buildings that sold for more than $200/sq.ft is 79.1%. If a you see a sales ad for a building that is asking for more than $200/sq.ft, what is the probability that the building is a residential building. Music and Exam Performance: Researcher believe that 75% of students (or more) can benefit from listening to music while studying for an exam. To verify this, they recruited 120 high school students from different grade levels (Freshmen to Senior) to participate in a study. The students were asked to take a test immediately after they studied a new subject in a room for three hours. The researchers asked students to repeat the process two times: once without listening to music and another time while listening to their preferred music. The order of the tests (with or without music) and the subjects were randomly assigned. The researchers recorded the difference between with-music and without-music scores to measure the impact of listening to music on score. In addition to the above information, they recorded students' gender. Use this information to answer the following questions titled Music and Exam Performance. 13) The response variable in this study is ____________, a) Music: whether a student listened to music or not. b) Score Change: the increase (decrease) in test score. c) Subject: the material that the student studied. d) Gender: the gender of the student. e) Grade Level: the student's school grade level (9th, 10th, 11th, 12th) (b) 14) The response variable is a _________ variable. a) Numerical (quantitative) b) Categorical (qualitative) (a)

20) The population of interest is ________ and the sample used in the study is _________. a) all high-school students b) all tests taken by high-school students c) 120 students who participated in the study d) 65 students who did better with music (a) and (c) 21) This study is an observational study. a) True b) False FALSE Statistic Class The following table shows the probabilities for randomly selecting a student from a 25- student class of statistics: Table 4. Proportions for a Class of 25 Graduating? Computer Sci. (Yes) Non-Computer Sci. (No) Total Graduating Yes (Senior) 28% 4% 32% No (Non-Senior) 52% 16% 68% Total Computer Sci. 80% 20% 100% Let 𝐺 represent the event that a randomly selected student in graduating, and 𝐶 represent the event that the selected student studies Computer Science. Use the above information to answer the following questions. 22) Match the probabilities with the events: a) 𝑷(𝑮) = b) 𝑷(? ? ) = c) 𝑷(𝑮 ∩ ?) = d) 𝑷(𝑮 ∪ ?) = 32% 20% 28% 84%

23) Consider these two events: A. Selecting a computer student if we draw from graduating students (seniors). B. Selecting a graduating student given the student studies Computer Science. Choose a proper notation from the following mathematical statements: a) 𝐺 b) 𝐶 c) 𝐺|𝐶 d) 𝐺 ∪ 𝐶 e) 𝐶|𝐺 f) 𝐺 ∩ 𝐶 A : (e), B: (c) The following histogram shows the age distribution of male patients who are diagnosed with Alzheimer's disease. The mean age is 76.66 years, and the standard deviation is 9.51 years. 24) Approximate the above distribution with a normal distribution by completing the x-axis values. [2 points]