Exponential Probability Between 5:00 PM and 6:00 PM, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 5:00 PM. F(t)=1-e^-0.15t
(a) Determine how many minutes are needed for the probability to reach 50%.
(b) Determine how many minutes are needed for the probability to reach 80%.

Question

Exponential Probability Between 5:00 PM and 6:00 PM, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 5:00 PM. F(t)=1-e^-0.15t
(a) Determine how many minutes are needed for the probability to reach 50%.
(b) Determine how many minutes are needed for the probability to reach 80%.

anonymous · Answer

weird i looked at this and thought it was the poisson distribution, but it i not

anonymous · Answer

$$1-e^{-0.15t}=.5$$ solve for $t$

anonymous · Answer

subtract 1 and get 
$$e^{-.15t}=.5$$ take the log to get 
$$-.15t=\ln(.5)$$ and finally divide by $-.15$ giving 
$$t=-\frac{\ln(.5)}{.15}$$

anonymous · Answer

second one is similar

anonymous · Answer

ok thank you @satellite73 
with an approximate solution of 4.62