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Using Technology In Exercises 17-22, use a symbolic
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Calculus: An Applied Approach (MindTap Course List)
- Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. 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. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?arrow_forward(USE R-Studio to solve this question) Concentration of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a log normal distribution. This is important when one considers issues regarding compliance to government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters θ=3.6 and ω = 0.5 a)Is this a valid probability density function? What is the relationship between the lognormal r.v. and the corresponding normal r.v.? Explain briefly. b)What is the probability that the concentration exceeds 15 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the same probability by using normal distribution and illustrate the probability on the normal pdf plot. c)What is the probability that the concentration is between 8 and 16 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the…arrow_forwardPDF = f(x) 2/x^3 for x>1 Question: - what is Probability ... P(x<4 or x>8)? - x such that P(X>x) ?arrow_forward
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