A supplier contract calls for a key dimension of a part to be between 1.96 and 2.04 centimeters. The supplier has determined that the standard deviation of its process, which
is normally distributed, is 0.04 centimeter.
a. If the actual mean of the process is 1.98, what fraction of parts will meet
specifications?
b. If the mean is adjusted to 2.00, what fraction of parts will meet specifications?
c. How small must the standard deviation be to ensure that no more than 2% of parts
are nonconforming, assuming the mean is 2.00?

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?