The taxi and takeoff time for commercial jets is a randomvariable x with a mean of 8.5 minutes and a standarddeviation of 3.1 minutes. Assume that the distribution of taxi andtakeoff times is approximately normal. You may assume that the jetsare lined up on a runway so that one taxies and takes offimmediately after the other, and that they take off one at a timeon a given runway.

(a) What is the probability that for 34 jets on a given runway,total taxi and takeoff time will be less than 320 minutes? (Roundyour answer to four decimal places.)


(b) What is the probability that for 34 jets on a given runway,total taxi and takeoff time will be more than 275 minutes? (Roundyour answer to four decimal places.)


(c) What is the probability that for 34 jets on a given runway,total taxi and takeoff time will be between 275 and 320 minutes?(Round your answer to four decimal places.)

It's true — sand dunes in Colorado rival sand dunes of the GreatSahara Desert! The highest dunes at Great Sand Dunes NationalMonument can exceed the highest dunes in the Great Sahara,extending over 700 feet in height. However, like all sand dunes,they tend to move around in the wind. This can cause a bit oftrouble for temporary structures located near the \"escaping\" dunes.Roads, parking lots, campgrounds, small buildings, trees, and othervegetation are destroyed when a sand dune moves in and takes over.Such dunes are called \"escape dunes\" in the sense that they moveout of the main body of sand dunes and, by the force of nature(prevailing winds), take over whatever space they choose to occupy.In most cases, dune movement does not occur quickly. An escape dunecan take years to relocate itself. Just how fast does an escapedune move? Let x be a random variable representingmovement (in feet per year) of such sand dunes (measured from thecrest of the dune). Let us assume that x has a normaldistribution with μ = 10 feet per year and σ =2.7 feet per year.

Under the influence of prevailing wind patterns, what is theprobability of each of the following? (Round your answers to fourdecimal places.)

(a) an escape dune will move a total distance of more than 90feet in 7 years


(b) an escape dune will move a total distance of less than 80 feetin 7 years


(c) an escape dune will move a total distance of between 80 and 90feet in 7 years