To help highway planners anticipate the need for road repairs and design future construction projects, data are collected on the estimated volume and weight of truck traffic on specific roadways (Transportation Planning Handbook, 2016) using specialized "weigh-in-motion" equipment. In an experiment involving the repeated weighing of a 27,907-pound truck, it was found that the weights recorded by the weigh-in-motion equipment were approximately normally distributed with a mean of 27,315 and a standard deviation of 628 pounds (Minnesota Department of Transportation). It follows that the difference between the actual weight and recorded weight, the error of measurement, is normally distributed with a mean of 592 pounds and a standard deviation of 628 pounds. [25 Points]

a.What is the probability that the weigh-in-motion equipment understates the truck's actual weight?

b.If a 27,907-pound truck was driven over the weigh-in-motion equipment 100 times, approximately how many times would the equipment overstate the truck's weight?

c.What is the probability that the error in the weight recorded by the weigh-in-motion equipment for a 27,907-pound truck exceeds 400 pounds?

d.It is possible to adjust (or calibrate) the weigh-in-motion equipment to control the mean measurement error. At what level should the mean error be set so the equipment will understate the weight of a 27,907-pound truck 50% of the time? Only 40% of the time?