A random variable follows the continuous uniform distribution between 160 and 340. Calculate the following quantities for the distribution. a) P(220less than or equalsxless than or equals290) b) P(160less than or equalsxless than or equals250) c) P(xgreater than190) d) What are the mean and standard deviation of this distribution?

a) 0.3889

b) 0.5

c) 0.8333

d) The mean is 250 and the standard deviation is 51.96.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability of finding a value of X higher than x is:

The probability of finding a value of X between c and d is:

The mean and the standard deviation are, respectively:

A random variable follows the continuous uniform distribution between 160 and 340.

This means that

a)

b)

c)

d)

The mean is 250 and the standard deviation is 51.96.

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.