Question

Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,500 skateboards and a standard deviation of 55 skateboards.

A. On what percent of the days last year did the factory produce 20,555 skateboards or fewer?
B. What percent of the days last year did the factory produce 20,610 skateboards or more?
C. On what percent of the days last year did the factory produce 20,445 skateboards or fewer?

Answer 1

(Use the normal distribution graph below to help you solve problems like this)

a) 34 + 34 + 13.5 + 2.35 + 0.15 = 84%

b) 2.35 + 0.15 = 2.5%

c) 13.5 + 2.35 + 0.15 = 16%

Answer 2

This can be solved by using the empirical rule for a normal distribution.
A. The number of skateboards given is one standard deviation above the mean. Approximately 68% of the data points lie within the range plus and minus one standard deviation of the mean. Therefore the required percentage is:
68 + 16 = 84%.
B. The given number of skateboards is two standard deviations above the mean. Approximately 95% of the data points lie within the range plus and minus two standard deviations of the mean. Therefore the required percentage is:
5/2 = 2.5%
C.The given number of skateboards is one standard deviations below the mean. Therefore the required percentage is:
16%.