Page 168 - Probability Demystified

CHAPTER 9 The Normal Distribution 157

Fig. 9-1.

EXAMPLE: The mean commuting time between a person’s home and office
is 24 minutes. The standard deviation is 2 minutes. Assume the variable is
normally distributed. Find the probability that it takes a person between
24 and 28 minutes to get to work.

SOLUTION:
Draw the normal distribution and place the mean, 24, at the center. Then
place the mean plus one standard deviation (26) to the right, the mean plus
two standard deviations (28) to the right, the mean plus three standard
deviations (30) to the right, the mean minus one standard deviation (22) to
the left, the mean minus two standard deviations (20) to the left, and the
mean minus three standard deviations (18) to the left, as shown in Figure 9-2.
Using the areas shown in Figure 9-1, the area under the curve between 24
and 28 minutes is 0.341 þ 0.136 ¼ 0.477 or 47.7%. Hence the probability that
the commuter will take between 24 and 28 minutes is about 48%.

Fig. 9-2.