5.3. Applications of the Normal Distribution http://www.ck12.org
- What is thez−score for the lower quartile in a standard normal distribution?
- The manufacturing process at a metal parts factory produces some slight variation in the diameter of metal
ball bearings. The quality control experts claim that the bearings produced have a mean diameter of 1.4 cm.
If the diameter is more than.0035 cm to wide or too narrow, they will not work properly. In order to maintain
its reliable reputation, the company wishes to insure that no more than 1/ 10 thof 1% of the bearings that are
made are ineffective. What should the standard deviation of the manufactured bearings be in order to meet
this goal? - Suppose that the wrapper of a certain candy bar lists its weight as 2.13 ounces. Naturally, the weights of
individual bars vary somewhat. Suppose that the weights of these candy bars vary according to a normal
distribution withμ= 2 .2 ounces andσ=.04 ounces.
a. What proportion of candy bars weigh less than the advertised weight?
b. What proportion of candy bars weight between 2.2 and 2.3 ounces?
c. What weight candy bar would be heavier than all but 1% of the candy bars out there?
d. If the manufacturer wants to adjust the production process so no more than 1 candy bar in 1000 weighs
less than the advertised weight, what should the mean of the actual weights be? (Assuming the standard
deviation remains the same)
e. If the manufacturer wants to adjust the production process so that the mean remains at 2.2 ounces and
no more than 1 candy bar in 1000 weighs less than the advertised weight, how small does the standard
deviation of the weights need to be??Review Answers
- e