4. Janet takes a bus to campus every weekday. Her bus arrives every 20 minutes. Suppose...

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4. Janet takes a bus to campus every weekday. Her bus arrives every 20 minutes. Suppose Janet shows up to the bus stop without looking at the schedule for the bus, so the amount of time she must wait for the bus is uniformly between 0 minutes and 20 minutes, with all of the times equally likely. Let X = amount of time Janet must wait for the bus (in minutes) a. How is X distributed? X ~ Uniform (0,20) b. Find the mean and standard deviation for Janet's waiting times. 0+20/2=10 = 20-0/sqr(12)=5.7735 C. Compute each of the following probabilities. In each case, include the probability statement, and a well drawn, labeled and shaded graph. | i. Find the probability that Janet has to wait more than 8 minutes for the bus. P(x>8)=(b-c)/(b-a) =(20-8)/(20-0) = 0.6 ii. Find the probability that Janet has to wait 15 to 20 minutes for the bus. P(15 4. Janet takes a bus to campus every weekday. Her bus arrives every 20 minutes. Suppose Janet shows up to the bus stop without looking at the schedule for the bus, so the amount of time she must wait for the bus is uniformly between 0 minutes and 20 minutes, with all of the times equally likely. Let X = amount of time Janet must wait for the bus (in minutes) a. How is X distributed? X ~ Uniform (0,20) b. Find the mean and standard deviation for Janet's waiting times. 0+20/2=10 = 20-0/sqr(12)=5.7735 C. Compute each of the following probabilities. In each case, include the probability statement, and a well drawn, labeled and shaded graph. | i. Find the probability that Janet has to wait more than 8 minutes for the bus. P(x>8)=(b-c)/(b-a) =(20-8)/(20-0) = 0.6 ii. Find the probability that Janet has to wait 15 to 20 minutes for the bus. P(15