Individual bottles of water are filled by a machine at a factory with an amount of water that is approximately normal with a mea
n of 505\,\text{mL}505mL505, start text, m, L, end text and a standard deviation of 10\,\text{mL}10mL10, start text, m, L, end text. A random sample of 161616 bottles is selected for a quality inspection. What is the probability that the mean amount of water in these 161616 bottles \bar x x ˉ x, with, \bar, on top is within 5\,\text{mL}5mL5, start text, m, L, end text of the population mean?
A function from a set to a set is a relation that assigns to each element in the set exactly one element in the set . The set is the domain (also called the set of inputs) of the function and the set contains the range (also called the set of outputs). On the other hand, a function has an inverse function if and only if passes the Horizontal Line Test for Inverse Functions. This test tells us that a function has an inverse function if and only if there is no any horizontal line that intersects the graph of at more than one point. So the function is called one-to-one. The graph of is shown below. As you can see, this function does not pass the Horizontal Line Test, therefore the inverse is not a function. However, let's find :
and this is not a function because there are elements in the set of inputs that match with two elements in the set of outputs.