Let X denote the distance (m) that an animal moves from its birth site to the fi
ID: 3134597 • Letter: L
Question
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 lambda = 0.01332. What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places.) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) What is the value of the median distance? (Round your answer to two decimal places.) Suppose a research paper states that the distribution of the daily sea-ia sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5lambdae^_lambdalxl for -infinity is given as 40.3 km. (Round your answers to four decimal places.) What is the value of the parameter lambda? What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?Explanation / Answer
14.
b)
Here, the mean is the same as the standard deviations,
u = sigma = 1/lambda = 1/0.01332 = 75.07507508
Hence,
u + 2*sigma = 75.07507508 + 2*75.07507508 = 225.2252252
The right tailed area in an exponential distribution is
P(x>x1) = e^(-x1/u)
As
x1 = critical value = 225.2252252
Then
Area = 0.049787068 [ANSWER]
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