Questions 4,5,6

8.4 Normal Distribution Confidence Intervals: Exercises 1. A laboratory scale is known to have a standard deviation of o = 0.001 gram in repeated weighings. Scale readings in repeated weighings are normally distributed, with mean equal to the true weight of the speci- men. Three weighings of a specimen give (in grams) 3.412, 3.414, 3.415 (a) Give a 95% confidence interval for the true weight of the specimen, rounding your final answer to four decimal places. [Hint: You will need to find the sample mean x.] (b) What is the lower bound of your confidence interval? What is the upper bound? (c) Based on the confidence interval you found, can you say the true weight of the specimen is 3.4123? EXPLAIN your answer using complete sentences. 2. Repeat exercise 1 with the confidence level being 90% instead of 95%. 3. Repeat exercise 1 with the confidence level being 99% instead of 95%. For the next three problems, assume you have x = 15, o = 3.24, and n = 30. 4. Find the confidence interval when the confidence level is 0.80. 5. Find the confidence interval when the confidence level is 0.85. 6. Now assume instead that n = 40. Find the confidence interval when the confidence level is 0.80