Please help with the following assignment (will give helpful rating):

2. A magazine reports that the average bowling score for league bowlers in the United States is 15? with a standard deviation of 12, and that the scores are approximately normally distributed. A. State the shape, the mean. and the standard deviation of the mean I- of 15 bowlers selected at random. Justify each statement by showing your work or identifying the theorem that tells you your answer is correct. {4 points} B. 1What'e the probability that a random sample of 15 bowlers would have an average score greater than 165? (5 points} C. what's the probability a random sample of 150 bowlers will have an average score greater than 165? [5 points) 3. The following is a histogram of the rst ten terms of a geometric distribution with p = .4. The mean of this distribution is 2.5 and the standard deviation is approximately 1.93. it. What's the shape of the distribution of sample means for simple random samples of size 5 drawn from this distribution? What are the mean and the standard deviation of the sampling distribution? (5 points) 3. What's the shape of the distribution of sample means for simple random samples of size 50 drawn from this distribution? {5 points} C. On average, how many trials will It take for the first success to occur? (4 points} 1. Annie is a basketball player who makes. an average, 65% of her free throws. Assume each shot is independent and the probability of making any given shot is .65. A. What's the probability Annie will miss three straight free throws before she makes one? {If you use a calculator to get your answer, write your answer in standard notation, not calculator notation.) (5 points) 3. During a season, Annie takes 140 free throws. 1What's the exact binomial probability she'll make at least 100 out of 140 of these throws? (4 points) C. For part B, are the conditions that permit you to use a normal approximation to the binomial satised? Explain. (5 points) D. Redo part B using a normal approximation, without continuity correction,r to the binomial. Draw a sketch of the situation; draw the distribution and shade the area representing the probability you're nding. (5 points} Note: If you use a graphing calculator, you don't need to calculate the z-scores. However, you should explain your answer in enough detail to show your instructor that you understand what you're doing. E. Redo part B using a normal approximation, lth continuity correction, to the binomial. (5 points) Note: If you use a graphing calculator, you don't need to calculate rscores, but do explain your answer in enough detail to show your instructor you understand what you're doing