A project completion time can be assumed to be represented by a normal distribut

Question

A project completion time can be assumed to be represented by a normal distribution curve. The project is expected to complete in 36 weeks with a path variance of 6.67. Base om the information provided, calculate:  

Calculate the probability that the project will be completed in 39 weeks or less

The probability that the project will be completed in between 33.5 and 38 weeks

With 95 percent probability, calculate the date the project can be expected to be completed

A project completion time can be assumed to be represented by a normal distribution curve. The project is expected to complete in 36 weeks with a path variance of 6.67. Base om the information provided, calculate:  

Calculate the probability that the project will be completed in 39 weeks or less

The probability that the project will be completed in between 33.5 and 38 weeks

With 95 percent probability, calculate the date the project can be expected to be completed

Explanation / Answer

Following to be noted :

Project mean = m = 36 weeks

Project standard deviation =Sd = Square root ( Project variance ) = Square root ( 6.67 ) = 2.58 weeks

Let Z value corresponding to probability that project will be completed in 39 weeks or less = Z1

M + Z1 x Sd = 39

Or, 36 + Z1 x 2.58 = 39

Or, 2,58.Z1 = 3

Or, Z1 = 3/2.58

Or, Z1 = 1.16 ( rounded to 2 decimal places )

Corresponding value of probability as derived from standard normal distribution table =0.87698

PROBABILITY THAT THE PROJECT WILL BE COMPLETED IN 39 WEEKS OR LESS = 0.87698

Probability that the project will be completed between 33.5 weeks and38 weeks

= Probability that the project will be completed in 38 weeks – Probability that the project will be completed in 33.5 weeks

Let Z value corresponding to probability that project will be completed in maximum 38 days = Z2

Z value corresponding to probability that the project will be completed in maximum 33.5 weeks = Z3

In such case ,

M + Z2 x Sd = 38

Or, 36 + 2.58.Z2 = 38

Or, 2.58.Z2 = 2

Or, Z2 = 2/2.58

Or, Z2 = 0.77 ( rounded to 2 decimal places )

Corresponding probability as derived from standard normal distribution table = 0.77935

Similarly ,

M + Z3 X Sd = 33.5

Or, 36 + 2.58 .Z3 = 33.5

Or, 2.58.Z3 =- 2.5

Or, Z3 = - 0.97 ( rounded to 2 decimal places )

Corresponding probability as derived from standard normal distribution table = 0.16602

Therefore ,

Probability that the project will be completed between 33.5 weeks and38 weeks

= Probability that the project will be completed in 38 weeks – Probability that the project will be completed in 33.5 weeks

= 0.77935 – 0.16602

= 0.6133

PROBABILITY THAT THE PROJECT CAN BE COMPLETED BETWEEN 33.5 AND 38 WEEKS = 0.6133

Z value for 95 percent probability = NORMSINV ( 0.95 ) = 1.6448

Therefore the date project can be expected to be completed with 95 percent probability

= 36 + 1.6448 x 2.58weeks

= 36 + 4.24

= 40.24

PROJECT CAN BE COMPLETED IN 40.24 WEEKS

PROBABILITY THAT THE PROJECT WILL BE COMPLETED IN 39 WEEKS OR LESS = 0.87698

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