Respuesta :
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X<x) = 0.95
We have to find the value of x such that the probability is 0.95
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 130}{10})=0.95[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<1.645)=0.95[/tex]
[tex]\displaystyle\frac{x - 130}{10} = 1.645\\x = 146.45 \approx 146.5[/tex]
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.
