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MATH 1280 Milestone 1 - 4_Introduction to Statistics (2022) – A Grade | MATH1280 Milestone_Introduction to Statistics BUNDLE

MATH 1280 Milestone 3_Introduction to Statistics (2020) – University of the People Tracie spins the four-colored spinner shown below. She records the total number of times the spinner lands on the c... olor red and constructs a graph to visualize her results. Which of the following statements is TRUE? • If Tracie spins the spinner 1,000 times, it would land on red close to 250 times. • If Tracie spins the spinner 1,000 times, the relative frequency of it landing on red will remain constant. • If Tracie spins the spinner 4 times, it will land on red at least once. • The theoretical probability of the spinner landing on red will change with every spin completed.RATIONALE If we make the assumption that the area of the colors represents the true proportion, then each color is equally weighted. Since there are four colors we would expect them to come up roughly 1/4 of the time. So on 1000 rolls the expected value = n*p = 1000*0.25 = 250. CONCEPT Law of Large Numbers/Law of Averages 2 Two sets A and B are shown in the Venn diagram below. Which statement is TRUE? • There are a total of 17 elements shown in the Venn diagram. • Set A has 12 elements. • Set B has 5 elements. •Sets A and B have 15 common elements. RATIONALE The number of elements of Set A is everything in Circle A, or 10+2 = 12 elements. The number of elements of Set B is everything in Circle B, or 5+2 = 7 elements, not 5 elements. The intersection, or middle section, would show the common elements, which is 2 elements, not 15 elements. To get the total number of items in the Venn diagram, we add up what is in A and B and outside, which is 10+2+5+3 = 20 elements, not 17 elements. CONCEPT Venn Diagrams 3 Using the Venn Diagram below, what is the conditional probability of event B occurring, assuming event A has happened [P(B|A)]? • 0.41 •0.63 • 0.24 • 0.77 RATIONALE To get the probability of B given A has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.41. The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65. CONCEPT Conditional Probability 4 The gender and age of Acme Painting Company's employees are shown below. Age Gender 23 Female 23 Male 24 Female 26 Female 27 Male 28 Male 30 Male31 Female 33 Male 33 Female 33 Female 34 Male 36 Male 37 Male 38 Female 40 Female 42 Male 44 Female If the CEO is selecting one employee at random, what is the chance he will select a male OR someone in their 40s? • 1/3 • 1/2 • 11/18 • 1/18 RATIONALE Since it is possible for an employee to be a male and a person in their 40s, these two events are overlapping. We can use the following formula:Of the 18 employees, there are 9 females and 9 males, so . There are a total of 3 people in their 40s, so . Of the people in their 40s, only one is male so . CONCEPT "Either/Or" Probability for Overlapping Events 5 Which of the following is a condition of binomial probability distributions? • All observations are mutually exclusive. • All observations are made randomly. • All observations made are dependent on each other. • All observations made are independent of each other. RATIONALE In the binomial distribution we always assume independence of trials. This is why we simply multiply the probability of successes and failures directly to find the overall probability. CONCEPT Binomial Distribution 6 La'Vonn rolled a die 100 times. His results are below. Number Times Rolled 1 182 20 3 15 4 17 5 14 6 16 What is the relative frequency for La'Vonn rolling a 3? Answer choices are rounded to the hundredths place. • 0.01 • 0.15 • 0.07 • 0.38 RATIONALE The relative frequency of a 3 is: CONCEPT Relative Frequency Probability/Empirical Method 7 For a math assignment, Jane has to roll a set of six standard dice and record the results of each trial. She wonders how many different outcomes are possible after rolling all six dice. What is the total number of possible outcomes for each trial? • 216• 46,656 • 7,776 • 36 RATIONALE We can use the general counting principle and note that for each step, we simply multiply all the possibilities at each step to get the total number of outcomes. Each die has 6 possible outcomes, so the overall number of outcomes for rolling 6 die with 6 possible outcomes each is: CONCEPT Fundamental Counting Principle 8 Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace. Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number. • 31% • 8% • 25% • 4% RATIONALESince the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the following formula: CONCEPT "Either/Or" Probability for Non-Overlapping Events 9 Colleen has 6 eggs, one of which is hard-boiled while the rest are raw. Colleen can't remember which of the eggs are raw. Which of the following statements is true? • The probability of Colleen selecting the hard-boiled egg on her first try is 1/5. • If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5. • If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/6. • The probability of Colleen selecting a raw egg on her first try is 1/6. RATIONALE The probability of choosing the hard-boiled egg is 1/6. If she cracks an egg and it is not the hard-boiled egg, then it becomes 1/5 on the next try because there are now only 5 eggs remaining and one has to be the hard-boiled egg as she did not pick it on the first try. CONCEPT Independent vs. Dependent Events 10 Eric is randomly drawing cards from a deck of 52. He first draws a red card, pla [Show More]

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