Problem 10 Bus Waiting Time [2 points] You show up at a bus stop to wait for a bus that comes by once per hour. You do not know what time the bus came by last. The arrival time of the next bus is a continuous uniform distribution [0,60] measured in minutes. Show your work answers in fractional format (a) Find the probability that you will wait between 15 and 20 minutes. (b) Find the probability that you will wait between 50 and 70 minutes. Problem 11 IQ of Smokers [2 points] Assume that you want to estimate the mean IQ score for the population of adults who smoke. How many smokers must be randomly selected for IQ tests if you want 99% condence that the sample mean is within 1 IQ point of the true population mean? Assume the population of IQ scores is normally distributed and has historically shown a standard deviation = 25. Show your work tojusti; your answer integer answer Problem 12 Tunnel Traffic [2 points] calculator In mountain country, major highways sometimes use tunnels instead of long, winding roads over high passes. However, too many vehicles in a tunnel at the same time can cause a hazardous situation. Traffic engineers are studying a long tunnel in Colorado. If x represents the time for a single vehicle to go through the tunnel, it is known that the x distribution has a mean u = 12.1 minutes and standard deviation o = 3.8 minutes under ordinary traffic conditions. From a histogram of these x values, it was found that the x distribution is mound-shaped with some symmetry about the mean. Engineers have calculated that, on average, vehicles should spend from 11 to 13 minutes in the tunnel. If the time is less than 11 minutes, traffic is moving too fast for safe travel in the tunnel. If the time is more than 13 minutes, there is a problem of bad air quality (too much carbon monoxide and other pollutants). Under ordinary conditions, there are about 83 vehicles in the tunnel at one time. What is the probability that the mean time for 83 vehicles in the tunnel will be from 11 to 13 minutes? answer to four decimal places Guiding Statement: circle answer Given x, find A! Given A, find x! Probability Statement: Calculator Function Used: Function Argument Inputs: correct sequence Calculator