Assume the time required to complete a product is normally distributed with a mean 3.2 hours and standard deviation .4 hours. How long should it take to complete a random unit in order to be in the top 10% (right tail) of the time distribution?

3.712 hours or more

Step-by-step explanation:

Let X be the random variable that denotes the time required to complete a product.

X is normally distributed.

Let x be the times it takes to complete a random unit in order to be in the top 10% (right tail) of the time distribution.

Then,

As,  [By z-table]

Then,

So, it will take 3.712 hours or more to complete a random unit in order to be in the top 10% (right tail) of the time distribution.

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.