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1.Can you help me explain the usefulness of Central Limit Theorem in solving problems involving sampling. And also the importance of the use of CLT in our daily life by creating own word problem, or formulating a new word problem.

2.There are 250 dogs at a dog show that weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 4 dogs are chosen at random, what is the probability that the average weight is greater than 8 pounds?

3.The number of driving miles before a certain kind of tire begins to show wear is on the average, 16,800 miles with a standard deviation of 3, 300 miles.

a.What is the probability that the 36 tires will have an average of less than 16,000 miles until the tires begin to wear out?

b.What is the probability that the 36 tires will have an average of more than 18,000 miles until the tires begin to wear out?

4.The average number of milligrams of cholesterol in a cup of 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 670mg?

b.If a sample of 10 cups of ice cream is selected, what is the probability that mean of the sample will be larger than 670 mg?

5.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?

6.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?

7.The average public elementary school has 486 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?