Assume that your statistics professor receives an average of five e-mail messages per day from students. if the number of messages approximates a poisson distribution, what is the probability that on a randomly selected day your professor will have five messages?

 Our required probability is 0.175.

Step-by-step explanation:

Since we have given that

Average of 5 e-mails messages per day.

so,

We need to find the probability that on a randomly selected day your professor will have 5 messages.

Let X be the number of messages in poisson distribution.

So, P(X=5) is given by

Hence, our required probability is 0.175.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.