http://www.ck12.org Chapter 6. Normal Distribution Curves
a) Between 67 g and 73 g lies 68% of the data. If 1,250 bags of chips are processed, 1, 250 × 0. 68 =850 bags will
have a mass between 67 g and 73 g.
b) 95%+ 2 .35%+ 0 .15%= 97 .5% of the bags of chips will have a mass greater than 64 grams.
Example C
The finishing times for people completing a half marathon in 2010 were normally distributed, with a mean of 130
minutes and a standard deviation of 20 minutes. If 1,400,000 people completed a half marathon in 2010, how many
people had finishing times between each of the following pairs of times?
a) 90 minutes and 150 minutes
b) 110 minutes and 130 minutes
c) 130 minutes and 190 minutes
a) Between 90 minutes and 150 minutes lies 13.5%+68%= 81 .5% of the data. This means that 1, 400 , 000 ×
0. 815 = 1 , 141 ,000 of the people who completed a half marathon in 2010 had a time between 90 minutes and 150
minutes.
b) Between 110 minutes and 130 minutes lies 34% of the data. This means that 1, 400 , 000 × 0. 34 = 476 ,000 of the
people who completed a half marathon in 2010 had a time between 110 minutes and 130 minutes.
c) Between 130 minutes and 190 minutes lies 34%+ 13 .5%+ 2 .35%= 49 .85% of the data. This means that
1 , 400 , 000 × 0. 4985 = 697 ,900 of the people who completed a half marathon in 2010 had a time between 130
minutes and 190 minutes.
Points to Consider
- Is the normal distribution curve the only way to represent data?
- The normal distribution curve shows the spread of the data, but it does not show the actual data values. Do
other representations of data show the actual data values?
Guided Practice
Sudoku is a very popular logic game of number combinations. It originated in the late 1800’s by the French press,
Le Siècle. The average times (in minutes) it takes those in a senior math class to complete a Sudoku puzzle are
normally distributed and are found below. Draw a normal distribution curve to represent this data. Determine what
time a student must complete a Sudoku puzzle in to be in the top 2.5%.