1.The time to wait for a particular rural bus is distributed uniformly from 0 to 75 minutes. 100 riders are randomly sampled and their waiting times are measured. The 90th percentile of the average waiting time (in minutes) for a sample of 100 riders is (approximately ______

2.Information text

A switching board receives a random number of phone calls. The expected number of calls is 5.3 per minute. Assume that the distribution of the number of calls is Poisson. The average number of calls per minute is recorded by counting the total number of calls received in one hour, divided by 60, the number of minutes in an hour. In the next 4 questions you are asked to apply the Normal approximation to the distribution of the sample average using this information. The answer may be rounded up to 3 decimal places of the actual value:

a)The expectation of the average is____

b)The standard deviation of the average is_____

c)The probability that the average is less than 5____

d)The probability that number of calls in a random minute is less than 5 isAnswer_____. (Note, the question is with respect to arandom minute, and not the average.)