Answer: 0.3413
Step-by-step explanation:
Given :Mean : [tex]\mu=60\text{ weeks}[/tex]
Standard deviation : [tex]\sigma = 5\text{ weeks}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 60 ,
[tex]z=\dfrac{60-60}{5}=0[/tex]
For x= 65 ,
[tex]z=\dfrac{65-60}{5}=1[/tex]
The p-value = [tex]P(0<z<1)=P(z<1)-P(z<0)[/tex]
[tex]= 0.8413447-0.5= 0.3413447\approx0.3413[/tex]
Hence, the probability that the project will take anywhere between 60 and 65 weeks to complete = 0.3413.
