Boxes are labeled as containing 600 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 8 g. (a) If the target weight is 600 g, what is the probability that the machine produces a box with less than 580 g of cereal? (Round your answer to three decimal places.) 0.087 (b) Suppose a law states that no more than 9% of a manufacturer's cereal boxes can contain less than the stated weight of 600 g. At what target weight should the manufacturer set its filling machine? (Round your answer to the nearest gram.) 585 X 9 Need Help? Read It . [-/2 Points] DETAILS SCALCET9 8.5.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The speeds of vehicles on a highway with speed limit 90 km/h are normally distributed with mean 105 km/h and standard deviation 10 km/h. (Round your answers to two decimal places.) (a) What is the probability that a randomly chosen vehicle is traveling at a legal speed? % (b) If police are instructed to ticket motorists driving 110 km/h or more, what percentage of motorist are targeted? % Let f(t) be the probability density function for the time it takes you to drive to school in the morning, where t is measured in minutes. Express the following probabilities as integrals. (If you need to use co or -co, enter INFINITY or - INFINITY, respectively.) (a) The probability that you drive to school in less than 15 minutes S f(t) dt (b) The probability that it takes you more than half an hour to get to school S f(t) dt 8. [-/2 Points] DETAILS SCALCET8 8.5.008. Consider the following function whose graph is shown. y 0.2 y= f(x) 0.1 0 2 4 8 10 x (a) Explain why the function whose graph is shown above is a probability density function. The integral of the function is 10. The values of both endpoints of the function are 0. The total area under the function is 1. The highest value of the function is 0.2. The derivative of the function is constant. (b) Use the graph to find the following probabilities. (Round your answers to three decimal places.) (i) P(X < 3) (ii) P(3 X 10) (c) Calculate the mean. (Round your answer to three decimal places.) MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER