6.0 7.0 8.0 9.0 Boxplot of sleep (hrs) Midterm Exam - MATH324: Probability and Statistics with Computing 1. [7 points] One of our students is tracking sleep (in hours) and productivity (in number of tasks completed). Here is the boxplot of their sleep: Please explain what summary statistics the boxplot shows. 2. [6 points] If out of our 30 students, 6 enjoy only playing sports, 7 enjoy only TV-based entertainment, and 10 enjoy neither, then what's the probability that if we select 9 different students at random, we will select 3 from each of the three groups? 3. [9 points] In our class, some our students really enjoy playing video games (V) and some really enjoy art (A). Say that about 34% enjoy video games, about 27% enjoy art, and 46% enjoy neither. a. Then what percent of students enjoy both video games and art? b. For these students, are enjoying video games and enjoying art independent events? 4. [6 points] Sometimes one of the keys to good photography is to take lots of pictures. Let's say someone has a 1/3 chance of taking a good photo independently of any other photo. a. If the photographer wants to produce 5 good photos for a gallery show they are part of, what is the probability that they will need to take as many as 50 photos? b. If the photographer takes 33 photos, what is the expected number of good photos they will produce?