Question: (12) Normal Distribution

1. Describe the various properties of the Normal Distribution, and what steps you would take to check whether or not a data set follows the normal distribution.
2. For the normal distribution, the mean plus and minus .86 standard deviations will include what percent of the observations? HINT: Use the Table.
3. The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 4.2 tons. What is probability that a truck will weigh less than 14.3 tons? Note the use of a sample.
4. Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a population standard deviation of 3,500 miles . For the entire population of these tires:
   1. What is the best estimate of the average tread life in miles?
   2. What is the probability that a tire will last 53,000 miles or more?

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