Final answer:
To find the probability that no car crosses the bridge in 30 minutes, you can use the Poisson distribution formula. Since the average number of cars crossing the bridge is 7 per hour, the probability is approximately 0.8904.
Step-by-step explanation:
To find the probability that no car crosses the bridge in 30 minutes, we can use the Poisson distribution formula. Since the average number of cars crossing the bridge is 7 per hour, we can calculate the rate parameter lambda by dividing the average by the number of minutes in an hour, which is 60. Lambda = 7/60 = 0.1167 cars per minute. The probability of no cars crossing the bridge in 30 minutes can be calculated using the Poisson distribution formula: P(X = 0) = (e^(-lambda) * lambda^0) / 0!
Substituting lambda = 0.1167 and X = 0:
P(X = 0) = (e^(-0.1167) * 0.1167^0) / 0! = (e^(-0.1167) * 1) / 1 = e^(-0.1167).
So, the probability that no car crosses the bridge in 30 minutes is e^(-0.1167) or approximately 0.8904.