Suppose you have a bag with 11 balls in it, and you have placed 11 buckets on the floor (where each bucket has a label affixed to it; say, the buckets are labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11). Now, consider the following experiment. You draw a ball from the bag, toss the ball into one of the buckets, and record the bucket in which the ball landed (for simplicity, assume that the ball has to land in a bucket; i.e., you cannot “miss” all of the buckets and hit the floor, or anything like that). You repeat this procedure until your bag of balls is empty (at which point the experiment has concluded). Let S denote the sample space for this experiment, and define the events E and F as follows. E: All of the balls are in one bucket at the conclusion of the experiment. F: No bucket is empty at the conclusion of the experiment. What is n(E)?

A psychology lab doing research in dreams has 4 rooms (1,2,3, and 4), each containing 2 beds (A and B). Three pairs of twins are being studied tonight. Each pair of twins will be assigned to one of the four rooms, and then each twin will be assigned a specific bed in the room. How many ways are there to organize the experiment? (i.e. How many ways are there to assign the 6 subjects to rooms and beds if each pair of twins must share the same room?) 24 8 192 48 12

2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:

james rolls a dice and flips a coin 150 times as part of an experiment.he records 80 heads,and 6 27 total times.on 55 occasions,he gets neither a head nor a 6.Complete the table below

Ethan has a bag that contains strawberry chews, apple chews, and lime chews. He performs an experiment. Ethan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Ethan performs the experiment 47 times. The results are shown below: A strawberry chew was selected 36 times. A apple chew was selected 9 times. A lime chew was selected 2 times.   If the experiment is repeated 600 more times, about how many times would you expect Ethan to remove a lime chew from the bag? Round your answer to the nearest whole number.

note: only need the answer for the last part about assumptions

1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…