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
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.
Get Answers For Free
Most questions answered within 1 hours.