The time required to make 1100 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 16 hours and a standard deviation of 3 hours. What is the probability that it will take more than 19 hours to make 1100 gallons of synthetic rubber?
[Notice that the "1100 gallons" has nothing to do with the problem]
We calculate the z-score for 19
We draw the normal curve and shade under the curve
to the right of z=1:
The percentage of the area that is shaded is what we are after.
Now you've probably learned that 34.1% of the area under
the normal curve lies between z=0 and z=1 and that 50% of
all of the area under the normal curve lies to the right
of z=0. So subtracting the 34.1% of the area between
z=0 and z=1 from 50% gives the percent of shaded area,
which is the probability that it will take more that 19
hours. 50%-34.1% = 15.9% is the desired probability, or,
expressed as a decimal, 0.159.
Edwin