The distance between flaws on a long cable is exponentially distributed with mean 12 m.

a. Find the probability that the distance between two flaws is greater than 15m.

b. Find the probability that the distance between two flaws is between 8 and 20 m.

c. Find the median distance.

d. Find the standard deviation of the distances.

e. Find the 65th percentile of the distances.

(a) The probability that the distance between two flaws is greater than 15 m is 0.2865.

(b) The probability that the distance between two flaws is between 8 and 20 m is 0.3246.

(c) The median is 8.322.

(d) The standard deviation is 12.

(e) The 65th percentile of the distances is 12.61 m.

Step-by-step explanation:

The random variable X can be defined as the distance between flaws on a long cable.

The random variable X is exponentially distributed with mean, μ = 12 m.

The parameter of the exponential distribution is:

The probability density function of X is:

(a)

Compute the  probability that the distance between two flaws is greater than 15 m as follows:

Thus, the probability that the distance between two flaws is greater than 15 m is 0.2865.

(b)

Compute the  probability that the distance between two flaws is between 8 and 20 m as follows:

Thus, the probability that the distance between two flaws is between 8 and 20 m is 0.3246.

(c)

The median of an Exponential distribution is given by:

Compute the median as follows:

Thus, the median is 8.322.

(d)

The standard deviation of an Exponential distribution is given by:

Compute the standard deviation as follows:

Thus, the standard deviation is 12.

(e)

Let x be 65th percentile of the distances.

Then, P (X < x) = 0.65.

Compute the value of x as follows:

Thus, the 65th percentile of the distances is 12.61 m.

step- i d k and i d c : )

you: : 0

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step-by-step explanation:

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