Summers Daniels
07/08/2024 · Senior High School

Between 12:00 PM and 1:00 PM, cars arrive at a bank's drive-thru at the rate of 18 cars per hour (0.3 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within \( t \) minutes of \( 12: 00 \) PM. Complete parts (a)-(c). \[ F(t)=1-e^{-0.3 t} \] (a) Determine how many minutes are needed for the probability to reach \( 30 \% \). About 1.19 minutes are needed for the probability to reach \( 30 \% \). (Round to two decimal places as needed.) (b) Determine how many minutes are needed for the probability to reach \( 90 \% \). About \( \square \) minutes are needed for the probability to reach \( 90 \% \). (Round to two decimal places as needed.)

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(a) About 1.19 minutes are needed for the probability to reach 30%. (b) About 7.68 minutes are needed for the probability to reach 90%.

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