Question 1: Probability 1.1 – {5 pts} If you roll two fair 6 sided dice, what is the probability of getting a 6, 7 or 8? 1.2 – {5 pts} If you flip a coin, roll a single 6 sided dice and draw a single card from a standard deck of cards (standard decks have 52 cards), what is the probability you will get a Heads and a 6 on the dice and an Ace from the deck of cards? 1.3 – {5 pts} Assume you have a small bag of marbles that contains 30 red marbles, 25 yellow marbles, 50 green marbles and 5 blue marbles. What is the probability you will draw a set of 6 marbles, without putting any back, in the following order: Red, Yellow, Red, Blue, Blue, Green? Question 2: Frequency Distribution and Histograms Sadly, at least from my perspective, the average person living in the United States only reads from an average of between 10 and 20 minutes a day. You do not actually need this for the problem, but I thought it was an interesting thing to know. Minutes Spent Reading Per Day: 18, 13, 16, 8, 18, 17, 14, 30, 14, 39, 43, 27, 33, 31, 34, 36, 32, 15 2.1 – {9 pts} For the above data on how much time people spend reading, please construct a Frequency Distribution. It should have about 7 intervals, and should include columns for both relative frequency and relative proportion. 2.2 – {6 pts} Please create a histogram for the above data. Make sure it is correctly labeled! 2.3 – {Extra Credit/Optional + 3 pts} Add and fill out the two columns for cumulative frequency and cumulative proportion to the frequency distribution. Question 3: Means and Standard Deviation Data Background: You are in charge of choosing a construction company to build a series of affordable housing complexes in your city, both for the homeless and underserved communities. The two construction companies that are in consideration are called the “Mavericks” and the “Dough-Bos”. You hire an independent firm to evaluate 12 previous constructions projects from each firm and give it a rating from 1 to 100, where the higher the number, the better overall quality of the project. Data: Mavericks: 50, 75, 73, 72, 82, 88, 97, 58, 35, 82, 58, 82 Dough-Bos: 65, 72, 62, 61, 72, 59, 55, 62, 69, 87, 58, 82 Question Particulars: 3.1 – {12 pts} Please calculate the mean and standard deviation for Mavericks. 3.2 – {12 pts} Please calculate the mean and standard deviation for the Dough-Bos For both of the above calculation sets, please clearly label the following: • Mean • Sum of Squares • Variance • Standard Deviation 3.3 – {3 pts} Based on the values you calculated for the mean and standard deviation for both construction companies, which company would you recommend? Please explain your answer. 3.4 – {Extra Credit/Optional + 5 pts} Are there any outliers in either of the two data sets? Question 4: Z Scores An epidemiologist (someone who studies diseases) has been keeping track of how long people suffer from the common cold. They found that the average time that people seem to report having physical discomfort is about 83 hours from when they notice symptoms to when they feel better. The standard deviation around this average is about 20 hours. Note: Please make sure to include a separate graph for each of the following parts of this question, and they particular section of the graph that the question is asking about should be shaded. Further, the axis at the bottom of each graph should be correctly labeled. Question Parts: 4.1 – {5 pts} What is the probability of a random person suffering from symptoms for more than 60 hours? 4.2 – {5 pts} What proportion of people suffer from symptoms for less than 48 hours? 4.3 – {10 pts} What is the probability of a random person suffering symptoms form anywhere between 67 and 112 hours? 4.4 – {10 pts} What proportion of people suffer symptoms from anywhere between 95 and 125 hours? 4.5 – {5 pts} What is the longest amount of time a person can report suffering from symptoms to be included in the 8% of shortest suffering individuals