Probability and Normal Distribution Exercises
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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?
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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?
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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Presentation Transcript
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?
