Question

a student whose earliest class on Tuesdays starts at 10 am. Before class, she finds a parking spot on average 5 mins.

A) if the time to find a parking spot is exponentially distributed, what is the standard deviation of time to find a parking spot? what about the Coefficient of Variation?

B) Also assume they walk from any parking spot in 4 mins. with this assumption at what time should they should arrive at the school so that 95% of the time they will not be late to class?

Answer 1

A)

this is exponential distribution with parameter β =5

mean μ =

=β =

5.00

standard deviation σ=

=β =

5.00

therefore coefficient of variation =( σ/μ)*100 =(5/5)*100 =100 %

B)

pth percentile =-β*ln(1-p)

therfore 95th percentile =-5*ln(1-95/100)=

14.9787~ 15 minute

therefore they must arrive (15+4 =19) minute earlier or at 9:41 am to not to be late to class,