3. [Montgomery, Runger, Hubele(2007).] A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is assumed to normal with standard deviation 20 mm. If the mean of a random sample of size 10 is 185 mm, construct a 99% confidence interval for u, the true average foam height of the new shampoo. . The average score for a standardized Mathematics examination of 100 randomly selected students from a certain high school is 84.8. If the score is a random variable with standard deviation 10, give a 90% confidence interval for u, the actual average score for the standardized Mathematics examination. 5. The mean height of a random sample of n = 25 of a certain tree is y = 145.6 cm. Assume that the tree height is approximately normal with standard deviation 20 cm. Construct a 98% confidence interval for the true mean tree height.2. Consider the following data taken from a normal population with standard deviation 0.2: y, = 0.99, y, = 0.87, y3 = 0.45, y, = 0.87, y, = 0.59. a. Give the point estimate of the population mean u based from the sample. Triance b. What is the standard error of the sample mean? C. Construct a 95% confidence interval for u. d. Construct a 80% confidence interval for u.1. Consider the following data taken from a normal population with variance 4: x, = 2.01, x, = 2.58, x, = 1.99, x, = 1.87, x, = 2.50, x = 1.65, x, = 2.9, x = 3.8. a. Give the point estimate of the population mean u based from the sample. b. What is the standard error of the sample mean? C. Construct a 99% confidence interval for M. d. Construct a 90% confidence interval for M