central limit theorem

pls show the solution

Let's see how well you understood our discussion. At this point, I want you to solve the following problems. Show your complete solution by following the step-by- step procedure. 1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is normally distributed. a. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 670 mg? b. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg? 2. In a study of the life expectancy of 400 people in a certain geographic region, the mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 68 years? 3. The average cholesterol content of a certain canned goods is 215 milligrams, and the standard deviation is 15 milligrams. Assume that the variable is normally distributed. If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be greater than 220 milligrams? 4. The average public elementary school has 468 students with a standard deviation of 87. If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is between 445 and 485?1. Do we always add or subtract from 0.50? Explain. 2. When do we add the corresponding area of the z-score to 0.50? 3. When do we add the two corresponding areas of the z-score?Directions: Read, analyze, and solve the problems below. Show your complete solutions. 1. There are 250 dogs at a dog show that weigh an average of 12 pounds, with a standard deviation of 3 pounds. If 4 dogs are chosen at random, what is the probability that the average weight is greater than 3 pounds? 2. The average number of pages in a novel is 326 with a standard deviation of 24 pages. If a sample of 50 novels is randomly chosen, what is the probability that the average number of pages in these books is between 310 and 331? 3. The number of driving miles before a certain kind of tire begins to show wear is on the average, 16,300 miles with a standard deviation of 3,300 miles. a. What is the probability that the 30 tires will have an average of less than 10,000 miles until the tires begin to wear out? b. What is the probability that the 30 tires will have an average of more than 18,000 miles until the tires begin to wear out? ACTIVITY Direction: Read the problems below then write your answer on a separate paper. 1. Determine the standard error of the mean for each of the following sample size n given the population standard deviation of 30. Round off your answer to the nearest hundredths. a. n = 5 b. n = 12 c. n = 28 d. n = 35 e. n = 40 6 2. Analyze the answers obtained in item number 1. What can you say about the relationship of the sample size and the standard error? 3. How does this relationship affect the distribution? 4. When do we obtain a good estimate of the mean? 5. When do we say that the mean is a poor estimate