Concept explainers
Use a symbolic
Find the standard deviation of the probability density function
What percent of the distribution lies within one standard deviation of the mean?
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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_forwardLet X be the number of minutes that it takes a random selected student to solve a mathematical problem. The probability density function of X is: 1)Find the mean of X. 2) Find the standard deviation of X.arrow_forward
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