Page 178 - Probability Demystified

CHAPTER 9 The Normal Distribution 167

Draw and label the normal distribution curve. Shade in the area. See
Figure 9-15.

Fig. 9-15.

Subtract the smaller area from the larger area, 0.758 0.136 ¼ 0.622.
Hence the probability that a randomly selected tire will last between 21,800
and 25,400 miles is 0.622 or 62.2%.

EXAMPLE: The average time it takes college freshmen to complete a
reasoning skills test is 24 minutes. The standard deviation is 5 minutes. If a
randomly selected freshman takes the exam, find the probability that he or
she takes more than 32 minutes to complete the test. Assume the variable
is normally distributed.

SOLUTION:

Find the z value for 32 minutes:

value mean 32 24 8
z ¼ ¼ ¼ ¼ 1:6
standard deviation 5 5

Draw the standard normal distribution and label it as shown. Shade the
appropriate area. See Figure 9-16.

Fig. 9-16.