The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is given by the following formula.t P = 0.87 (a) What is the limiting value of P?
The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is given by the following formula.t P = 0.87 (a) What is the limiting value of P?
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![The headway \( h \) is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability \( P \) that the headway is at least \( t \) seconds is given by the following formula:
\[ P = 0.8^t \]
**(a) What is the limiting value of \( P \)?**
[Text box] (Incorrect)
**Explain what this means in practical terms.**
This means that the probability of finding very large headways is [Dropdown box selected: small].
**(b)** The headway \( h \) can be calculated as the quotient of the spacing \( f \) in feet, which is the average distance between vehicles, and the average speed \( v \), in feet per second, of traffic. Thus, the probability that spacing is at least \( f \) feet is the same as the probability that the headway is at least \( f/v \) seconds. Use function composition to find a formula for the probability \( Q \) that the spacing is at least \( f \) feet.
*Note*: Your formula will involve both \( f \) and \( v \).
\[ Q = \]
[Text box]
**(c)** If the average speed is 90 feet per second, what is the probability that the spacing between two vehicles is at least 41 feet? (Round your answer to the nearest whole number.)
[Text box] %](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74894f78-ccb5-452f-bebb-59c8a1f546c3%2Fd36adaea-ad6a-4cdf-9b28-62e458543cc2%2Fpememth_processed.png&w=3840&q=75)
Transcribed Image Text:The headway \( h \) is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability \( P \) that the headway is at least \( t \) seconds is given by the following formula:
\[ P = 0.8^t \]
**(a) What is the limiting value of \( P \)?**
[Text box] (Incorrect)
**Explain what this means in practical terms.**
This means that the probability of finding very large headways is [Dropdown box selected: small].
**(b)** The headway \( h \) can be calculated as the quotient of the spacing \( f \) in feet, which is the average distance between vehicles, and the average speed \( v \), in feet per second, of traffic. Thus, the probability that spacing is at least \( f \) feet is the same as the probability that the headway is at least \( f/v \) seconds. Use function composition to find a formula for the probability \( Q \) that the spacing is at least \( f \) feet.
*Note*: Your formula will involve both \( f \) and \( v \).
\[ Q = \]
[Text box]
**(c)** If the average speed is 90 feet per second, what is the probability that the spacing between two vehicles is at least 41 feet? (Round your answer to the nearest whole number.)
[Text box] %
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