The table below shows the distance y, in miles, traveled by a truck in x hours: Time (x)
(hours) 1 2 3 4
Distance (y)
(miles) 50 100 150 200

Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance traveled by the truck. [Choose the value of the correlation coefficient from 1, 0.8, 0.5, 0.02.]

Part B: What is the value of the slope of the graph of distance versus time between 3 and 4 hours, and what does the slope represent? (3 points)

Part C: Does the data in the table represent correlation or causation? Explain your answer.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.