An automatic machine produces on average, 10% of its components outside of the tolerance required. In a sample of 10 components from this machine, determine the probability of having two components outside of the tolerance required by assuming a binomial distribution.

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval. 3 f(x)=x²; [0,8] 512 E(X)= 8 X

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? Explain what this means in practical terms. This means that the probability of finding very large headways is small (b) The headway 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 fand v. Q = (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…

What is “fractional error” for the following formula? Z= 2/3 X2Y3  ,  X= 7m , Y= 4m,   σx=0.2m  ,  σy=0.1m σZ=?