Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 15 trains per hour (0.25 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t
Minutes of 7:00 AM. $$F ( t ) = 1 - e ^ { - 0.25 t }$$ Determine how many minutes are needed for the probability to reach 20%.
A) $0.89 \mathrm {~min}$
B) $2.35 \mathrm {~min}$
C) $5.34 \mathrm {~min}$
D) $4.12 \mathrm {~min}$

Question

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 15 trains per hour (0.25 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t
Minutes of 7:00 AM. $$F ( t ) = 1 - e ^ { - 0.25 t }$$ Determine how many minutes are needed for the probability to reach 20%. 
A) $0.89 \mathrm {~min}$
B) $2.35 \mathrm {~min}$
C) $5.34 \mathrm {~min}$
D) $4.12 \mathrm {~min}$

Quizplus · Accepted Answer

To find the time $t$ when the probability $F(t)$ reaches 20% (or 0.20), we set the equation $1 - e^{-0.25t} = 0.20$ and solve for $t$. Rearranging the equation gives $e^{-0.25t} = 0.80$. Taking the natural logarithm of both sides results in $-0.25t = \ln(0.80)$, and solving for $t$ gives $t = \frac{\ln(0.80)}{-0.25}$, which calculates to approximately $0.89$ minutes.

Choose the One Alternative That Best Completes the Statement or Answers