Question

Your company is considering submitting a bid on a major project. You determine that the expected completion time is 130 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution applies. You wish to set the due date for the project such that there is a 95 percent chance that the project will be finished by this time. What due date should be set?
a. 108.0
b. 160.4
c. 146.5
d. 135.0
e. none of the above

Answer 1

Answer:

Option C) 146.5

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 130 weeks

Standard Deviation, σ = 10 weeks

We are given that the distribution of completion time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(X<x) = 0.95

We have to find the value of x such that the probability is 0.95

P(X < x)  

$P( X < x) = P( z < \displaystyle\frac{x - 130}{10})=0.95$  

Calculation the value from standard normal z table, we have,  

$P(z$

$\displaystyle\frac{x - 130}{10} = 1.645\\x = 146.45 \approx 146.5$  

The project should be completed in 146.5 weeks or less.

Hence, 146.5 weeks should be set the due date such that there is a 95 percent chance that the project will be finished by this time.