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 162 degrees? b) What is the probability that the defect is found between 0 and 81 degrees or between 279 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

Solution:

We are given that the random variable follows uniform distribution with a = 0 and b = 360.

a) What is the probability that the defect is found between 0 and 162 degrees?

Here, we have to find P(0<X<162)

P(c<X<d) = (d – c) / (b – a)

P(0<X<162) = (162 – 0) / (360 – 0) = 162/360 = 0.45

The required probability is 0.450.

b) What is the probability that the defect is found between 0 and 81 degrees or between 279 and 360 degrees?

Here, we have to find P(0<X<81) + P(279<X<360)

P(c<X<d) = (d – c) / (b – a)

P(0<X<81) = (81 – 0) / (360 – 0) = 81/360 = 0.225

P(279<X<360) = (360 – 279) / (360 – 0) = 81/360 = 0.225

P(0<X<81) + P(279<X<360) = 0.225 + 0.225 = 0.450

The required probability is 0.450.