Question

Using? PERT, Adam Munson was able to determine that the expected project completion time for the construction of a pleasure yacht is 22 ?months, and the project variance is 9.

?a) The probability that the project will be completed in 13 months? = nothing ?(round your response to four decimal? places).

?b) The probability that the project will be completed in 21 months? = nothing ?(round your response to four decimal? places).

?c) The probability that the project will be completed in 25 months? = nothing ?(round your response to four decimal? places).

?d) The probability that the project will be completed in 31 months? = nothing ?(round your response to four decimal? places).

?e) The due date that yields a? 95% chance of completion? = nothing months ?(round your response to two decimal? places).

Answer 1

Given are following data :

Expected project completion time = m = 22 months

Project standard deviation = Sd = square root ( Variance ) = Square root ( (9 ) = 3

1. M + Z value of probability of completion in 13 months x Sd = 13

Or, 22 + 3.Z = 13

Or, 3.Z = 13 – 22

Or, 3.Z = - 9

Or, Z = - 9/3 = - 3

Corresponding probability for Z =- 3 as derived from standard normal distribution table = 0.00135 ( 0.0014 rounded to 4 decimal places)

PROBABILITY THAT THE PROJECT WILL BE COMPLETED IN 13 MONTHS = 0.0014

1. M + Z value for probability that project will be completed in 21 months x Sd = 21

Or, 22 + 3.Z = 21

Or, 3.Z = 21 – 22

Or, 3.Z = - 1

Or, Z = - 0.33

Corresponding probability for Z = - 0.33 as derived from standard normal distribution table = 0.3707

PROBABILITY THAT THE PROJECT WILL BE COMPLETD IN 21 MONTHS = 0.3707

1. M + z value that probability that project will be completed in 25 months x Sd = 25

Or, 22 + 3.Z = 25

Or, 3.Z = 3

Or, Z = 1

Corresponding probability for Z = 1 as derived from standard normal distribution table = 0.84134

PROBABILITY THAT THE PROJECT WILL BE COMPLETED IN 25 MONTHS = 0.84134

1. M + z value that the project will be completed in 31 months x Sd = 31

Or, 22 + 3.Z = 31

Or, 3.Z = 9

Or, Z = 3

Corresponding probability for Z = 3 as derived from standard normal distribution table = 0.99865

PROBABILITY THAT THE PROJECT WILL BE COMPLETED IN 31 MONTHS = 0.99865

1. 95% chance of completion mean probability of 0.95 of completion

Corresponding Z value for probability of 0.95 = NORMSINV ( 0.95 ) = 1.6448

The due data that yields 95 % chance of completion

= m + Z x Sd

= 22 + 1.6448 x 3

= 22 + 4.934

= 26.9344 ( 26.93 months rounded to 2 decimal places )

ANSWER :26.93 MONTHS