Question

A contractor estimates the probabilities for the number of weeks required to complete a certain type of construction project which takes 11 to 15 weeks to complete as follows:

Completion Time (Weeks)	11	12	13	14	15
Probability	X	0.25	0.35	0.10	X

Find X.

Select one:

a. 0.20

b. 0.30

c. Cannot be determined from the information given

d. 0.15

Answer 1

The given probability distribution table is:

Completion time weeks	11	12	13	14	15
Probability	X	0.25	0.35	0.10	X

Let ‘X’ be the missing values.

Assume P(11) = P(12) = X.

Find the missing value of X by using the condition that the total of all the probabilities equal 1.

P( 11 ) + P(12) + P(13) + P(14) + P(15) = 1

X + 0.25 + 0.35 + 0.10 + X = 1

2X+ 0.70 = 1

2X = 1 – 0.70

2X= 0.30

X = 0.30/2

X = 0.15

Thus, the complete probability distribution table is,

Completion time weeks	11	12	13	14	15
Probability	0.15	0.25	0.35	0.10	0.15

Since sum of all probabilities corresponding to completion time of each week is equal to 1, so the value of X is 0.15

Therefore, the correct option is d. 0.15.