Homework SourseThe time it takes a hiker to spot a deer is exponentially di
The time it takes a hiker to spot a deer is exponentially distributed with a mean of 22 minutes. Find the:
(a) probability it will take over 30 minutes for her to spot a deer.
(b) 20th percentile for the time it takes her to spot a deer
(c) standard deviation in the time it takes her to spot the next deer.
Please show the steps on how to do each problem. Thank you!
Solution
Given X follows Exponential distribution with mean =22
F(x)=1-exp(-x/22) for x>0
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(a) probability it will take over 30 minutes for her to spot a deer.
P(X>30)=1-(1-exp(-30/22))=0.2557292
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(b) 20th percentile for the time it takes her to spot a deer
F(x)=1-exp(-x/22) =0.2
--> exp(-x/22) =1-0.2=0.8
--> -x/22 = log(0.8)
So x= -22*log(0.8)=4.909158
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(c) standard deviation in the time it takes her to spot the next deer.
standard deviation =22
