The distance between major cracks in a highway follows an exponential distribution with a mean of 20 miles. What is the standard deviation o

Question

The distance between major cracks in a highway follows an exponential distribution with a mean of 20 miles. What is the standard deviation of the distance between two major cracks

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Skylar 7 hours 2021-09-15T04:59:38+00:00 1 Answer 0

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    2021-09-15T05:00:54+00:00

    Answer:

    20

    Step-by-step explanation:

    Let X be the exponentially distributed random variable with the given mean E(X)=20

    #To find the standard deviation, we first determine lambda,\lambda:

    20=E(X)=\frac{1}{\lambda}\\\\\\\lambda=\frac{1}{20}=0.05

    We then find standard deviation using the formula:

    std(X)=\sqrt{\frac{1}{\lambda^2}}\\\\=\sqrt{\frac{1}{\0.05^2}}\\\\=20

    Hence, the standard deviation of the distance between two major cracks is 20

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