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.)

Answer 1

Explanation:

Given that 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.

X is U(0,360)

a)
`P(0<x<81) = (81)/(360) =0.225`

b)
`P(0<x<99 or 261<x<360)\\=P(0<x<99 )+P(261<x<360)\\=(99)/(360) +(99)/(360) \\=0.55`