Defects can occur anywhere on the wheel of a car during the manufacturing proces

Question

Defects can occur anywhere on the wheel of a car during the manufacturing process. If X is the angle where the defect? occurs, measured from a reference? line, then X can be modeled as a uniform random variable on the interval from 0 to 360 degrees.

?a) What is the probability that the defect is found between 0 and 81 ?degrees? ?

b) What is the probability that the defect is found between 0 and 99 degrees or between 261 and 360 ?degrees?

?a) The probability is ---------. ?(Round to three decimal places as? needed.)

?b) The probability is ---------. ?(Round to three decimal places as? needed.)

Explanation / Answer

If defects are uniformly distributed, then the probability of a defect in a given angle range is the ratio of that range to 360°.

a) (81-0)/360 = 9/40 = 0.225

b) ((99-0)+(360-261))/360 = 198/360 = 0.55

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