Statistics and Probability, Central limit theorem lesson.

let's Analyze Direction: Solve the following problem below. 1. At a large pubtishing company. the mean age of proof readers is 36.2 years, and the standard deviation is 3.7 years. Assume the variable is normally distributed. a. If the proof reader from the company is randomly selected, find the probability that his or her age will be between 36 and 37.5 years. b. If a random sample of 15 proof readers is selected. find the probability that the mean age of the proof readers in the sample will be between 36 and 37.5 years. 2. The average cholesterol content of a certain brand of eggs is 215 milligrams. and the standard deviation is 15 milligrams. Assume the variable is normally distributed. a. If a single egg is selected. find the probability that the mean of the sample will be greater than 220 milligrams. b. If a sample of 25 eggs is selected. find the probabiity that the mean of the sample will be larger 220 milligrams. let's Evaluate .. '~ Direction: Solve the following problems below. Problem 1: The average labor cost for car repairs for a large chain of car repair shops is P520. The standard deviation is P40. Assume the variable 5 normally distributed. a. If a store is selected at random, nd the probability that the labor cost will range between P450 and P530. b. If 15 stores are elected at random. find the probability that the mean of the sample will be between P450 and P530. c. Which answer is larger? Explain why? Problem 2: The average monthly salary of teachers in the Philippines is P25 000. Assume that the salaries were normally distributed for a certain group of teachers, and the standard deviation of this group was P2 000. a. Find the probability that a randomly selected individual earned less than P27 000. b. Find the probability that, for a randomly selected sample of 20 individuals. the mean salary was less than P27 000. 0. Why is the probability for b is higher than the probability for a? Problem 3: Assume that the mean systolic blood pressure of ncmtai adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume that the variable is normally distributed. a. If an individual is selected, nd the probability that the individuals pressure will be between 118 and 121.8 mm Hg. b. If a sample of 20 adults is randomly selected1 find the probability that the sample mean will be between 118 and 121.8 mm Hg. c. Why is the answer to a is smaler than the answer in b