In the game Dungeons and Dragons (DnD) players roll a 20 sided die to determine the outcome of events (for example: do they successfully deceive the ruler or does the ruler see through their lie). Answer the following questions about the following dataset which displays one player's rolls (25 rolls). data: 15, 20, 4, 1, 5, 4, 8, 20, 3, 16, 20, 4, 6, 10, 11, 20, 7, 15, 16, 2, 17, 4, 18, 20, 1 (a) (1 point) Is this data quantitative or qualitative? (b) (1 point) We discussed two sub-categories of quantitative data and two subcategories of qualitative. Which of the four sub-categories of data are these data? (c) (3 points) Compute the sample mean, median, and mode of this dataset. (d) (2 points) Draw a histogram to visualize the dataset. (consider using a binwidth of 2) (e) (3 points) When a player rolls a 20 they automatically succeed in their task. What is the distribution of automatic successes when using a fair die (Note: a fair die is a die that has equal probability of rolling each number) (include the parameter values). (f) (3 points) What is the expected value (mean) and variance of the distribution of auto- matic successes (rolling a 20 on a 20-sided die)? (g) (2 points) Compute the probability of rolling exactly as many 20's as this player rolled when rolling 25 dice that each have 20 sides. (h) (5 points) DnD players are notoriously superstitious about their dice. Complete a six step hypothesis test to determine if we have sufficient evidence that the proportion of 20's that this player rolled is high enough to conclude that this is not a fair die at a = 0.01. (Comment: the sample size is small, so the normal approximation has a lot of error here)