Between 12:00 PM and 1:00 PM, cars arrive at a local bank\'s drive-thru at the r

Question

Between 12:00 PM and 1:00 PM, cars arrive at a local bank's drive-thru at the rate of 10 cars per hour (0.17car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM: Upper F left parenthesis t right parenthesis equals 1 minus e Superscript negative 0.17 t

Use this information to answer the questions given below in parts (a)-(b).

(a) What is the probability that a car will arrive within 5 minutes of 12:00 PM (that is,before 12 : 05 PM)?

F(5)=         (Round to three decimal places as needed.)

(b) What is the probability that a car will arrive within 10 minutes of 12:00 PM (that is commabefore 12 : 10 PM)?

F(10)=        (Round to three decimal places as needed.)

Explanation / Answer

Upper F left parenthesis t right parenthesis equals 1 minus e Superscript negative 0.17 t

F(t) = 1 -e^(-0.17t)

a) F(5) Plug t = 5 in formula above.

F(5) = 1- e^(-0.17*5) = 1 - 0.4274 = 0.572

b) F(10) 1 - e^(-0.17*10) = 1 - 0.1826 =0.817

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