Statistics
a companys manufacturing process uses 500 gallons of water at a time. a "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. to meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical. because a fine is charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water. the machine's output can be described by a normal model with standard deviation 4.2 ppm. what percent of the batches of water discharged exceed the 80 ppm standard?
a. 3.89%
b. 1.17%
c. 88.3%
d. 11.7%
e. 8.83%
and show how you get it

D

Step-by-step explanation:

Im sorry, I dont have access to a Z table right now.

When you describe a normal distribution the values between - 1 and +1 deviation standard are the 68% of the total. So dividing in the mean, you have 34% from the mean to - 1 deviation standard and 34% from the mean to +1 deviation standard. Since the mean is actually the 50%, all values lower than the mean equal 50% and values between mean and +1 deviation standard equal 34%, therefore all values lower than +1 deviation standard equal 50+34 = 84%

Mean + 1 deviation standard = 75 +4.2 = 79.2, so batches that exceed 79.2 ppm 16%

( Its 84% below +1 deviation so above +1 deviation is 100 - 84 = 16)

Since you are looking for the percent that exceeds 80 it should be a bit less than 16, so 11.7%.

Like I said I dont have a Z Table right now.

In order to use the z table, you need to calculate Z, as follows:

Z = (x - mean)/(standard deviation)

Z = (80 - 75)/4.2

With that number you search the probability in a Z table thats it.

g

step-by-step explanation:

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.