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 15 m. b.) Find the probability that the distance between two flaws is between 8 and 20 m. c.) Find the median distance between flaws.

a) P = 0.29

b) P = 0.32

c) median = 8.3

Explanation:

We have an average distance of 12 m, therefore:

12 = 1/λ

Clearing λ:

λ = 1/12

let "x" be the distance between the flaws, we have:

a)

Let P be the probability that the distance between two flaws is 15 m:

P(x>15) = 1-P(x<15) = 1-(1-e^(λ*x)) = e^(-15/12) = 0.29

b)

Let P be probability that the distance between two flaws is between 8 and 20 m:

P(8<x<20) = P(x<20) - P(x<8) = (1-e^(-20/12)) - (1-e^(-8/12)) = e^(-8/12) - e^(-20/12) = 0.32

c)

The median distance between flaws is equal to:

P(x<median) = 0.5

1-e^(-median/12) = 0.5

e^(-median/12) = 0.5

-median/12 = ln(0.5)

median = ln(0.5) * (-12) = 8.3

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.