F(t) =1-e^(-0.2t)?

Between 12pm to 1pm cars arrive at a bank%26#039;s drive-thru at the rate of 12 cars per hour(0.2 per minute). the following formula from statistics can be used to determine the probability that a car will arrive within (t) minutes of 12pm. F(t) =1-e^(-0.2t)

A. What is the probability a car will arrive within 5 minutes of 12pm.

B. How many minutes are needed for the probability to reach 30%. That is solve F(t)=0.3

F(t) =1-e^(-0.2t)?yes loans

A. Can also be applied as a Poisson distribution as the expected waiting time for a car is 5 minutes. P(X = 0 | lambda = 1) = [(e^-1)*1^1]/1! = e^-1 = 0.36 approx.

So there is approx. a 0.64 chance at least one car arrives in 5 minutes.

B. 0.3 = 1 - e^-0.2t

e^-0.2t = 0.7

0.2t = -ln(0.7)

t = -ln(0.7) / 0.2 = -5ln(0.7)