Probability and Normal Distribution Exercises
Solving exercises related to normal distribution and probability, including calculating probabilities based on mean and standard deviation, determining minimum guaranteed mileage for a tire company, and interpreting test scores. Utilizes data on IQ test scores and tire mileage to illustrate concepts.
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EXERCISE Suppose scores on an IQ test are normally distributed. If the test has a mean of 100 and a standard deviation of 10. What is the probability that a person who takes the test will score less than 90? What is the probability that a person who takes the test will score between 90 and 110? What is the probability that a person who takes the test will score between 82.5 and 90?
EXERCISE Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67,900 with a standard deviation of 2,050 miles and that the distribution of miles follows the normal probability distribution. It wants to set the minimum guaranteed mileage so that no more than 4 percent of the tires will have to be replaced. What minimum guaranteed mileage should Layton announce?
