Consider a continuous random variable x,which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________.
A)0.75
B)1.00
C)0.50
D)0.075

Question

Quizplus · Accepted Answer

Since the continuous random variable is uniformly distributed between 65 to 85, the probability density function (PDF) is a constant value over this range. Therefore, the area under the PDF between any two values of x will give the probability of x taking on a value in that range.

To find the probability of x taking on a value between 75 to 90, we need to find the area under the PDF between these two values. However, the PDF is only defined between 65 to 85, so any values outside this range will have a PDF of 0.

Therefore, we need to find the area under the PDF between 75 to 85 and add the area under the PDF between 85 to 90, which is:

(85-75)/(85-65) + 0 = 0.50

So the probability of x taking on a value between 75 to 90 is 0.50 or 50%.

Consider a Continuous Random Variable X,which Is Uniformly Distributed Between