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 15 m.

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.

Step 1 of 6</p>

In a long cable the distance between flaws is exponentially distributed with mean 12 m

The mean of exponential distribution is=12

Then =0.0833

The pmf of Exponential distribution is

The CDF of exponential distribution is

Step 2 of 6</p>

a) We have to find the probability that the distance is greater than 15 m

Then P(X>15)=1-P(X15)

=1-(1-)

=

=0.2866

Hence the probability that the distance is greater than 15 m is 0.2866

Step 3 of 6</p>

b) We have to find the probability that the distance is between 8 and 20 meters

Then P(8=P(X

=(1-)-(1-)

=-

=

=0.5136 - 0.189

=0.3246

Hence the probability that the distance is between 8 and 20 meters is 0.3246