Customers pulling up to the drive-in window at the local burger joint experience

Question

Customers pulling up to the drive-in window at the local burger joint experience a wait from 1 minute and 30 seconds to 6 minutes and 10 seconds to receive their order. The distribution of time to complete an order follows the uniform distribution.

a-1) What are the values for a and b in minutes?
a-2) What are the values for a and b in seconds?

b-1) What is the mean time in minutes to complete the order?

b-2) What is the mean time in seconds to complete the order?

c-1) What is the standard deviation in minutes for completed orders?
c-2 What is the standard deviation in seconds for completed orders?

d-1) What percent of the orders take more than 4 minutes to complete?
d-2) What percent of the orders take more than 240 seconds to complete?

e) Does it matter whether you calculate the answers in Minutes or Seconds? Explain

Explanation / Answer

a-1) value of a =1+30/60 =1.5 minute ; b=6+10/60 =6.1667 minute

a-2) a =60+30 =90 seconds ; b=6*60+10=370 seconds

b-1) mean time in minutes =(1.5+6.1667)/2 =3.8333 minutes

b-2) mean time in second =(90+370)/2 =230

c-1) std deviation =(b-a)/(12)1/2 =1.3472

c-2) std deviation =(b-a)/(12)1/2 =80.829

d-1) percent of the orders take more than 4 minutes to complete =(6.1667-4)/(6.1667-1.5) =0.4643 ~46.43%

d-2) percent of the orders take more than 240 seconds to complete =(370-240)/(370-90)=0.4643~ 46.43%

e) as sample space for both distribution are proportional to each other and they both are measuring the same event for which favourable space is in same proportion therefore it does not matter whether you calculate the answers in Minutes or Seconds

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.