Let x denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. suppose that for banner-tailed kangaroo rats, x has an exponential distribution with parameter l 5 .01386 (as suggested in the article "competition and dispersal from multiple nests," ecology, 1997: 873–883). a. what is the probability that the distance is at most 100 m? at most 200 m? between 100 and 200 m? b. what is the probability that distance exceeds the mean distance by more than 2 standard deviations? c. what is the value of the median distance? devore, jay l.. probability and statistics for engineering and the sciences (p. 175). cengage learning. kindle edition.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?