1. Random samples of size n were taken from populations given below. Given your knowledge of the underlying distributions, determine the means and standard deviations of the sampling distributions a. Unknown distribution with \"n = 36,1: = 10.52 = 9 b. A normal distribution with n = 8.11 = 120, 3 = 4 c. A binomial distribution with n = 25,?1 2 0.50 d. A Poisson distribution with El = 4.11 = 16 2. Suppose a random sample of size 25 observations is selected from a population that is normally distributed with mean 105 and standard deviation equal to 12. a. Give the mean and standard deviation of the sampling distribution of the sample mean b. Find the probability that x-bar exceeds 110. c. Find the probability that the sample mean deviates from the population mean by no more than 4. 3. An advertiser claims that the average percentage of brown M&Ms candies in a package of milk chocolate M&Ms is 13%. Suppose you randomly select a package that contains 55 pieces and determine the proportion of brown candies in the package. a. What is the approximate distribution of the sample proportion of brown candies in a package that contains 55 candies? b. What is the probability that the sample percentage of brown candies is less than 20%? c. What is the probability that the sample percentage exceeds 35%? Within what range would you expect the sample proportion to lie about 95% of the time? 4. Suppose that the number of parking tickets for parking on the street given out on average in a month is 512. Suppose that we sample 256 weeks and the average number of parking tickets for parking in the street per week was found to be 130. a. How many parking tickets for parking on the street would you expect to be written per week assuming that there are four weeks per month? b. What is the sampling distribution for the average number of parking tickets for parking in the street per week {include the mean and standard deviation] c. What is the probability that you get more than 130 parking tickets per week for parking on the street on average