1. (Level 2; Computer Problem) Use R Commander to perform the following tasks. (a) Generate data sets of n observations from normally distributed random variables using 7 = 10, 100, 1000, 10000. (b) For each of the generated data seta in part (a) i. construct a histogram. ii. create normal probability plots. (c) Load the data given in the file LABprobl . txt into R Commander. Construct a histogram and a normal probability plot. Would you agree with the statement that the data was generated from a normally distributed random variable? Why or why not? 2. (Level 2) Consider a hypothetical population of dogs in which there are four possible weights, all of which are equally likely: 42, 48, 52, or 58 pounds. If a sample of size 2 is drawn from this population what is the sampling distribution of the total weight of the two selected dogs? That is, what are the possible values for the total and what are the probabilities associated with each of those values? 3. (Level 2) In a certain population of fish, the lengths of the individual fish follow approximately a normal distribution with mean 54.0 mm and standard deviation 4.6 mm. Suppose a random sample of four fish is chosen from the population. Find the probability that (a) all four fish are between 51 and 60 mm long; (b) the mean length of the four fish is between 51 and 60 mm. 4. (Level 3) A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) using the binomial distribution formula; (b) using the normal approximation; (e) using the normal approximation with continuity correction