Question

A construction company has to complete a project no later than 4 months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. It is currently believed that the probabilities of these four possibilities are .1, .6, .2, and .1, respectively. What is the probability that the project was completed sooner than expected

Answer 1

Answer:

The probability that the project was completed sooner than expected = 1

Step-by-step explanation:

Given four different variables:

X =(2, 2.5, 3, 3.5)

The probabilities of these variables are 0.1, 0.6, 0.2, 0.1 respectively.

Therefore,

P(X = 2) = 0.1

P(X = 2.5) = 0.6

P(X = 3) = 0.2

P(X = 3.5) = 0.1

For this project to be completed sooner than expected, it should be completed before 4 months.

I.e: P(X<4)

Therefore

P(X<4) = P(X=2)+P(X=2.5)+P(X=3)+P(X=3.5)

P(X<4) = 0.1 + 0.6 + 0.2 + 0.1

PX<4) = 1

The probability that the project was completed sooner than expected is 1.

Since it has a probability of 1, it is certain the job was completed sooner than expected.