Need help to solve this please Autos arrive at a toll plaza located at the entra

Question

Need help to solve this please

Autos arrive at a toll plaza located at the entrance to a bridgeat the rate of 50 per minute during the 5:00-6:00 p.m. hour. If anauto has just arrived,

a. what is the probability that the next auto will arrive within3 seconds (0.05 minute)?

b. what is the probability that the next auto will arrive within1 second (0.0167 minute)?

c. What are your answers to (a) and (b) if the rate of arrivalof autos is 60 per minute?

d. What are your answers to (a) and (b) if the rate of arrivalof autos is 30 per minute?

Explanation / Answer

exponential with mean = 1/25 minute

f (x) = (25)e^(-25x)

F(x) = 1 - e^(-25x)

a ) P(X < 0.05) = F(0.05) = 1 - e^(-0.05*25) = 0.7135

b) P(X < 0.0167) = F(0.0167) = 1 - e^(-0.0167*25) = 0.3413

c ) for a) F(0.05) = 1 - e^(-0.05*60) = 0.95

b) F(0.0167) = 1 - e^(-0.0167*60) = 0.6328

d ) for a) F(0.05) = 1 - e^(-0.05*30) = 0.77687

b) F(0.0167) = 1 - e^(-0.0167*30) = 0.394

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