Closing time of train doors. A private railway company in Sweden runs a night train service in from Trelleborg to Malmö from midnight to 6 am. While the company wants the train’s doors to close 30 seconds before it is scheduled to leave, the actual closing time x is random, anywhere between 25 and 45 seconds before the train is due to leave. Suppose x has a uniform probability distribution.

a. Is the time at which the doors close before departure a discrete or a continuous random variable? Explain.

b. Graph the frequency function for x, the closing time of the doors before the train’s departure.

c. Find the mean and standard deviation for the distribution graphed in part

b, and locate the mean and the interval m { s on the graph.

d. Find P1x Ú 402.

e. Find P1x 6 262.

f. Find P130 … x … 412. g. What is the probability that for each of the next two night trains, the doors close more than 38 seconds before the scheduled departure? Assume that the amount of time before the doors close on one train is independent of the amount of time before the doors close on another train.